From 4f6d858a331d21f5bd4faddc431f515d7d10a136 Mon Sep 17 00:00:00 2001 From: LanMai Date: Sun, 27 Dec 2015 09:26:18 +0800 Subject: [PATCH] OpenSIM Matlab code OpenSIM Matlab code --- OpenSIM manual.pdf | Bin 0 -> 1657034 bytes SIMbasic/ApodizationFunction.m | 30 ++++ SIMbasic/ApproxFreqDuplex.m | 30 ++++ SIMbasic/IlluminationFreqF.m | 38 ++++ SIMbasic/IlluminationPhaseF.m | 14 ++ SIMbasic/MergingHeptaletsF.m | 68 +++++++ SIMbasic/ModulationFactor.m | 86 +++++++++ SIMbasic/OBJparaOpt.m | 47 +++++ SIMbasic/OBJpowerPara.m | 48 +++++ SIMbasic/OTFdoubling.m | 17 ++ SIMbasic/OTFedgeF.m | 13 ++ SIMbasic/OTFmaskShifted.m | 13 ++ SIMbasic/PCMfilteringF.m | 143 +++++++++++++++ SIMbasic/PCMseparateF.m | 64 +++++++ SIMbasic/PatternPhaseOpt.m | 12 ++ SIMbasic/PhaseKai2opt.m | 46 +++++ SIMbasic/PsfOtf.m | 34 ++++ SIMbasic/SIMimagesF.m | 282 ++++++++++++++++++++++++++++++ SIMbasic/SIMo.m | 206 ++++++++++++++++++++++ SIMbasic/SIMplot.m | 84 +++++++++ SIMbasic/SeparatedComponents2D.m | 22 +++ SIMbasic/TripletSNR0.m | 66 +++++++ SIMbasic/WoFilterCenter.m | 57 ++++++ SIMbasic/WoFilterSideLobe.m | 54 ++++++ SIMbasic/testpat.tiff | Bin 0 -> 1048710 bytes SIMexpt/ApodizationFunction.m | 30 ++++ SIMexpt/ApproxFreqDuplex.m | 28 +++ SIMexpt/BgNormalization0.m | 39 +++++ SIMexpt/IlluminationFreqF.m | 38 ++++ SIMexpt/IlluminationPhaseF.m | 14 ++ SIMexpt/MergingHeptaletsF.m | 65 +++++++ SIMexpt/ModulationFactor.m | 86 +++++++++ SIMexpt/OBJparaOpt.m | 48 +++++ SIMexpt/OBJpowerPara.m | 48 +++++ SIMexpt/OTF.tif | Bin 0 -> 524410 bytes SIMexpt/OTFdoubling.m | 17 ++ SIMexpt/OTFedgeF.m | 13 ++ SIMexpt/OTFmaskShifted.m | 13 ++ SIMexpt/OTFpost.m | 20 +++ SIMexpt/PCMfilteringF.m | 157 +++++++++++++++++ SIMexpt/PCMseparateF.m | 62 +++++++ SIMexpt/PatternPhaseOpt.m | 13 ++ SIMexpt/PhaseKai2opt.m | 46 +++++ SIMexpt/SIMo.m | 88 ++++++++++ SIMexpt/SIMplot.m | 84 +++++++++ SIMexpt/SeparatedComponents2D.m | 22 +++ SIMexpt/TripletSNR0.m | 66 +++++++ SIMexpt/WoFilterCenter.m | 57 ++++++ SIMexpt/WoFilterSideLobe.m | 54 ++++++ SIMexpt/sim01z4.tif | Bin 0 -> 14181792 bytes TIRFbasic/ApodizationFunction.m | 30 ++++ TIRFbasic/Ifreq2opt.m | 49 ++++++ TIRFbasic/IlluminationFreqTIRF.m | 71 ++++++++ TIRFbasic/Kai2Opt.m | 38 ++++ TIRFbasic/MergingHeptaletsF.m | 67 +++++++ TIRFbasic/ModulationFactor.m | 86 +++++++++ TIRFbasic/OBJparaOpt.m | 47 +++++ TIRFbasic/OBJpowerPara.m | 48 +++++ TIRFbasic/OTFdoubling.m | 17 ++ TIRFbasic/OTFedgeF.m | 13 ++ TIRFbasic/OTFmaskShifted.m | 13 ++ TIRFbasic/PCMfilteringF.m | 146 ++++++++++++++++ TIRFbasic/PCMseparateF.m | 57 ++++++ TIRFbasic/PsfOtf.m | 34 ++++ TIRFbasic/SIMimagesF.m | 281 +++++++++++++++++++++++++++++ TIRFbasic/SIMo.m | 104 +++++++++++ TIRFbasic/SIMplot.m | 84 +++++++++ TIRFbasic/SeparatedComponents2D.m | 22 +++ TIRFbasic/TripletSNR0.m | 66 +++++++ TIRFbasic/WoFilterCenter.m | 57 ++++++ TIRFbasic/WoFilterSideLobe.m | 54 ++++++ TIRFbasic/testpat.tiff | Bin 0 -> 1048710 bytes TIRFexpt/ApodizationFunction.m | 30 ++++ TIRFexpt/BgNormalization0.m | 39 +++++ TIRFexpt/Ifreq2opt.m | 56 ++++++ TIRFexpt/IlluminationFreqTIRF.m | 71 ++++++++ TIRFexpt/Kai2Opt.m | 37 ++++ TIRFexpt/MergingHeptaletsF.m | 65 +++++++ TIRFexpt/ModulationFactor.m | 86 +++++++++ TIRFexpt/OBJparaOpt.m | 47 +++++ TIRFexpt/OBJpowerPara.m | 48 +++++ TIRFexpt/OTF.tif | Bin 0 -> 524410 bytes TIRFexpt/OTFdoubling.m | 17 ++ TIRFexpt/OTFedgeF.m | 13 ++ TIRFexpt/OTFmaskShifted.m | 13 ++ TIRFexpt/OTFpost.m | 20 +++ TIRFexpt/PCMfilteringF.m | 172 ++++++++++++++++++ TIRFexpt/PCMseparateF.m | 57 ++++++ TIRFexpt/SIMo.m | 94 ++++++++++ TIRFexpt/SIMplot.m | 84 +++++++++ TIRFexpt/SeparatedComponents2D.m | 22 +++ TIRFexpt/TripletSNR0.m | 66 +++++++ TIRFexpt/WoFilterCenter.m | 57 ++++++ TIRFexpt/WoFilterSideLobe.m | 54 ++++++ TIRFexpt/sim01z4.tif | Bin 0 -> 14181792 bytes 95 files changed, 5114 insertions(+) create mode 100644 OpenSIM manual.pdf create mode 100644 SIMbasic/ApodizationFunction.m create mode 100644 SIMbasic/ApproxFreqDuplex.m create mode 100644 SIMbasic/IlluminationFreqF.m create mode 100644 SIMbasic/IlluminationPhaseF.m create mode 100644 SIMbasic/MergingHeptaletsF.m create mode 100644 SIMbasic/ModulationFactor.m create mode 100644 SIMbasic/OBJparaOpt.m create mode 100644 SIMbasic/OBJpowerPara.m create mode 100644 SIMbasic/OTFdoubling.m create mode 100644 SIMbasic/OTFedgeF.m create mode 100644 SIMbasic/OTFmaskShifted.m create mode 100644 SIMbasic/PCMfilteringF.m create mode 100644 SIMbasic/PCMseparateF.m create mode 100644 SIMbasic/PatternPhaseOpt.m create mode 100644 SIMbasic/PhaseKai2opt.m create mode 100644 SIMbasic/PsfOtf.m create mode 100644 SIMbasic/SIMimagesF.m create mode 100644 SIMbasic/SIMo.m create mode 100644 SIMbasic/SIMplot.m create mode 100644 SIMbasic/SeparatedComponents2D.m create mode 100644 SIMbasic/TripletSNR0.m create mode 100644 SIMbasic/WoFilterCenter.m create mode 100644 SIMbasic/WoFilterSideLobe.m create mode 100644 SIMbasic/testpat.tiff create mode 100644 SIMexpt/ApodizationFunction.m create 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SIMexpt/sim01z4.tif create mode 100644 TIRFbasic/ApodizationFunction.m create mode 100644 TIRFbasic/Ifreq2opt.m create mode 100644 TIRFbasic/IlluminationFreqTIRF.m create mode 100644 TIRFbasic/Kai2Opt.m create mode 100644 TIRFbasic/MergingHeptaletsF.m create mode 100644 TIRFbasic/ModulationFactor.m create mode 100644 TIRFbasic/OBJparaOpt.m create mode 100644 TIRFbasic/OBJpowerPara.m create mode 100644 TIRFbasic/OTFdoubling.m create mode 100644 TIRFbasic/OTFedgeF.m create mode 100644 TIRFbasic/OTFmaskShifted.m create mode 100644 TIRFbasic/PCMfilteringF.m create mode 100644 TIRFbasic/PCMseparateF.m create mode 100644 TIRFbasic/PsfOtf.m create mode 100644 TIRFbasic/SIMimagesF.m create mode 100644 TIRFbasic/SIMo.m create mode 100644 TIRFbasic/SIMplot.m create mode 100644 TIRFbasic/SeparatedComponents2D.m create mode 100644 TIRFbasic/TripletSNR0.m create mode 100644 TIRFbasic/WoFilterCenter.m create mode 100644 TIRFbasic/WoFilterSideLobe.m create mode 100644 TIRFbasic/testpat.tiff create 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+wo = w/2; +if ( DoubleMatSize>0 ) + t = 2*w; + u = linspace(0,t-1,t); + v = linspace(0,t-1,t); + OTF2 = zeros(2*w,2*w); + OTF2(wo+1:w+wo,wo+1:w+wo) = OTFo; + clear OTFo +else + OTF2 = OTFo; + clear OTFo +end \ No newline at end of file diff --git a/SIMexpt/OTFedgeF.m b/SIMexpt/OTFedgeF.m new file mode 100644 index 0000000..8148030 --- /dev/null +++ b/SIMexpt/OTFedgeF.m @@ -0,0 +1,13 @@ +function Kotf = OTFedgeF(OTFo) + +w = size(OTFo,1); +wo = w/2; + +OTF1 = OTFo(wo+1,:); +OTFmax = max(max(abs(OTFo))); +OTFtruncate = 0.02; +i = 1; +while ( abs(OTF1(1,i)) Kotf; \ No newline at end of file diff --git a/SIMexpt/OTFpost.m b/SIMexpt/OTFpost.m new file mode 100644 index 0000000..2498868 --- /dev/null +++ b/SIMexpt/OTFpost.m @@ -0,0 +1,20 @@ +function OTFo = OTFpost(OTFo) +%% AIM: To flaten out the peripheral rippling frequencies + +OTFo = OTFo./max(OTFo(:)); + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +w = size(OTFo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Cv = (X-wo) + 1i*(Y-wo); +Ro = abs(Cv); + +Zmask = (Ro>(Kotf+20)).*(Ro(wo-10)); +OTFo = OTFo.*(1-Zperi) + OTFperi.*Zperi; \ No newline at end of file diff --git a/SIMexpt/PCMfilteringF.m b/SIMexpt/PCMfilteringF.m new file mode 100644 index 0000000..2e3fbd4 --- /dev/null +++ b/SIMexpt/PCMfilteringF.m @@ -0,0 +1,157 @@ +function [fDof,fDp2,fDm2,npDo,npDp,npDm,Mm,DoubleMatSize]... + = PCMfilteringF(fDo,fDp,fDm,OTFo,OBJparaA,kA) + +% AIM: obtaining Wiener Filtered estimates of noisy frequency components +% INPUT VARIABLES +% fDo,fDp,fDm: noisy estimates of separated frequency components +% OTFo: system OTF +% OBJparaA: object power parameters +% kA: illumination vector +% OUTPUT VARIABLES +% fDof,fDp2,fDm2: Wiener Filtered estimates of fDo,fDp,fDm +% npDo,npDp,npDm: avg. noise power in fDo,fDp,fDm +% Mm: illumination modulation factor +% DoubleMatSize: parameter for doubling FT size if necessary + +w = size(OTFo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Cv = (X-wo) + 1i*(Y-wo); +Ro = abs(Cv); + +% suppressing out-of-focus signal of off-center components using +% G is a notch-filter (determined heuristically) +G = 1 - exp(-0.05*Ro.^1.2); +fDp = fDp.*G; +fDm = fDm.*G; + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +Aobj = OBJparaA(1); +Bobj = OBJparaA(2); + +% Wiener Filtering central frequency component +SFo = 1; +co = 1.0; +[fDof,npDo] = WoFilterCenter(fDo,OTFo,co,OBJparaA,SFo); + +% modulation factor determination +Mm = ModulationFactor(fDp,kA,OBJparaA,OTFo); + +%% Duplex power (default) +kv = kA(2) + 1i*kA(1); % vector along illumination direction +Rp = abs(Cv-kv); +Rm = abs(Cv+kv); +OBJp = Aobj*(Rp.^Bobj); +OBJm = Aobj*(Rm.^Bobj); +k3 = round(kA); +OBJp(wo+1+k3(1),wo+1+k3(2)) = 0.25*OBJp(wo+2+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+2+k3(2))... + + 0.25*OBJp(wo+0+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+0+k3(2)); +OBJm(wo+1-k3(1),wo+1-k3(2)) = 0.25*OBJm(wo+2-k3(1),wo+1-k3(2))... + + 0.25*OBJm(wo+1-k3(1),wo+2-k3(2))... + + 0.25*OBJm(wo+0-k3(1),wo+1-k3(2))... + + 0.25*OBJm(wo+1-k3(1),wo+0-k3(2)); + +% Filtering side lobes (off-center frequency components) +SFo = Mm; +[fDpf,npDp] = WoFilterSideLobe(fDp,OTFo,co,OBJm,SFo); +[fDmf,npDm] = WoFilterSideLobe(fDm,OTFo,co,OBJp,SFo); + +%% doubling Fourier domain size if necessary +DoubleMatSize = 0; +if ( 2*Kotf > wo ) + DoubleMatSize = 1; % 1 for doubling fourier domain size, 0 for keeping it unchanged +end +if ( DoubleMatSize>0 ) + t = 2*w; + to = t/2; + u = linspace(0,t-1,t); + v = linspace(0,t-1,t); + [U,V] = meshgrid(u,v); + fDoTemp = zeros(2*w,2*w); + fDpTemp = zeros(2*w,2*w); + fDmTemp = zeros(2*w,2*w); + OTFtemp = zeros(2*w,2*w); + fDoTemp(wo+1:w+wo,wo+1:w+wo) = fDof; + fDpTemp(wo+1:w+wo,wo+1:w+wo) = fDpf; + fDmTemp(wo+1:w+wo,wo+1:w+wo) = fDmf; + OTFtemp(wo+1:w+wo,wo+1:w+wo) = OTFo; + clear fDof fDpf fDmf OTFo w wo x y X Y + fDof = fDoTemp; + fDpf = fDpTemp; + fDmf = fDmTemp; + OTFo = OTFtemp; + clear fDoTemp fDpTemp fDmTemp OTFtemp +else + t = w; + to = t/2; + u = linspace(0,t-1,t); + v = linspace(0,t-1,t); + [U,V] = meshgrid(u,v); +end + +% Shifting the off-center frequency components to their correct location +fDp1 = fft2(ifft2(fDpf).*exp( +1i.*2*pi*(kA(2)/t.*(U-to) + kA(1)/t.*(V-to)) )); +fDm1 = fft2(ifft2(fDmf).*exp( -1i.*2*pi*(kA(2)/t.*(U-to) + kA(1)/t.*(V-to)) )); +%{ +figure; +mesh(log(abs(fDp1))) + +pp = 3; +figure; +hold on +plot(u-to,log(abs(fDof(to+pp,:))),'go-','LineWidth',2,'MarkerSize',6) +plot(u-to,log(abs(fDp1(to+pp,:))),'o--','LineWidth',2,'MarkerSize',4) +grid on +box on +% kk +%} + +%% phase matching +Cv = (U-to) + 1i*(V-to); +Ro = abs(Cv); +Rp = abs(Cv-kv); +k2 = sqrt(kA*kA'); + +% frequency range over which corrective phase is determined +Zmask = (Ro < 0.8*k2).*(Rp < 0.8*k2); + +% corrective phase +Angle0 = angle( sum(sum( fDof.*conj(fDp1).*Zmask )) ); + +% phase correction +fDp2 = exp(+1i*Angle0).*fDp1; +fDm2 = exp(-1i*Angle0).*fDm1; + +%% for visual verification +%{ +pp = 3; +figure; +hold on +plot(u-to,angle(fDof(to+pp,:)).*180/pi,'o-','LineWidth',2,'MarkerSize',8) +plot(u-to,angle(fDp1(to+pp,:)).*180/pi,'ro-','LineWidth',2,'MarkerSize',8) +plot(u-to,angle(fDp2(to+pp,:)).*180/pi,'go--','LineWidth',2,'MarkerSize',6) +grid on +box on +figure; +hold on +plot3(u-to,real(fDof(to+1,:)),imag(fDof(to+1,:)),'o-','LineWidth',2,'MarkerSize',8) +plot3(u-to,real(fDp1(to+1,:)),imag(fDp1(to+1,:)),'ro-','LineWidth',2,'MarkerSize',8) +plot3(u-to,real(fDp2(to+1,:)),imag(fDp2(to+1,:)),'go--','LineWidth',2,'MarkerSize',6) +grid on +box on + +ff1 = fDof.*conj(fDp1); +ff2 = fDof.*conj(fDp2); +figure; +hold on +plot(u-to,angle(ff1(to+pp,:)).*180/pi,'ro-','LineWidth',2,'MarkerSize',8) +plot(u-to,angle(ff2(to+pp,:)).*180/pi,'go--','LineWidth',2,'MarkerSize',6) +grid on +box on +%} \ No newline at end of file diff --git a/SIMexpt/PCMseparateF.m b/SIMexpt/PCMseparateF.m new file mode 100644 index 0000000..2ec4c3d --- /dev/null +++ b/SIMexpt/PCMseparateF.m @@ -0,0 +1,62 @@ +function [fDo,fDp,fDm,kA]... + = PCMseparateF(S1aTnoisy,S2aTnoisy,S3aTnoisy,OTFo) +% AIM: obtaining the noisy estimates of three frequency components +% INPUT VARIABLES +% S1aTnoisy,S2aTnoisy,S3aTnoisy: 3 raw SIM images with identical +% illumination pattern orientation +% but different phase shifts +% OTFo: system OTF +% OUTPUT VARIABLES +% fDo,fDp,fDm: noisy estimates of separated frequency components +% kA: (averaged) illumination frequency vector + +w = size(S1aTnoisy,1); +wo = w/2; + +%% Determination of illumination frequency vectors +[k1a] = IlluminationFreqF(S1aTnoisy,OTFo); +[k2a] = IlluminationFreqF(S2aTnoisy,OTFo); +[k3a] = IlluminationFreqF(S3aTnoisy,OTFo); + +% mean illumination frequency vector +kA = (k1a + k2a + k3a)/3; + +%% determination of illumination phase shifts +[phase1A] = IlluminationPhaseF(S1aTnoisy,kA); +[phase2A] = IlluminationPhaseF(S2aTnoisy,kA); +[phase3A] = IlluminationPhaseF(S3aTnoisy,kA); +% for display in command window +phaseA = [phase1A; phase2A; phase3A]; +phaseA*180/pi + +% computing PSFe for edge tapering SIM images +PSFd = real(fftshift( ifft2(fftshift(OTFo.^3)) )); +PSFd = PSFd/max(max(PSFd)); +PSFd = PSFd/sum(sum(PSFd)); +h = 30; +PSFe = PSFd(wo-h+1:wo+h,wo-h+1:wo+h); + +% edge tapering raw SIM images +S1aTnoisy = edgetaper(S1aTnoisy,PSFe); +S2aTnoisy = edgetaper(S2aTnoisy,PSFe); +S3aTnoisy = edgetaper(S3aTnoisy,PSFe); + + +fS1aTnoisy = fftshift(fft2(S1aTnoisy)); +fS2aTnoisy = fftshift(fft2(S2aTnoisy)); +fS3aTnoisy = fftshift(fft2(S3aTnoisy)); + +%% Separating the three frequency components +phaseShift0 = phase1A; +phaseShift = [phase2A; phase3A]; +[fDo,fDp,fDm] = SeparatedComponents2D(... + phaseShift,phaseShift0,fS1aTnoisy,fS2aTnoisy,fS3aTnoisy); +%% for visual verification +%{ +figure; +mesh(log(abs(fDo))) +figure; +mesh(log(abs(fDp))) +figure; +mesh(log(abs(fDm))) +%} diff --git a/SIMexpt/PatternPhaseOpt.m b/SIMexpt/PatternPhaseOpt.m new file mode 100644 index 0000000..0376834 --- /dev/null +++ b/SIMexpt/PatternPhaseOpt.m @@ -0,0 +1,13 @@ +function CCop = PatternPhaseOpt(phaseA,S1aTnoisy,k2fa) + +w = size(S1aTnoisy,1); +wo = w/2; + +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); + +sAo = cos( 2*pi*(k2fa(2).*(X-wo)+k2fa(1).*(Y-wo))./w + phaseA ); +% S1aTnoisy = real( ifft2(fftshift(fS1aTnoisy)) ); +S1aTnoisy = S1aTnoisy - mean2(S1aTnoisy); +CCop = -sum(sum(S1aTnoisy.*sAo)); \ No newline at end of file diff --git a/SIMexpt/PhaseKai2opt.m b/SIMexpt/PhaseKai2opt.m new file mode 100644 index 0000000..1046bdf --- /dev/null +++ b/SIMexpt/PhaseKai2opt.m @@ -0,0 +1,46 @@ +function [CCop] = PhaseKai2opt(k2fa,fS1aTnoisy,OTFo,OPT) +% Aim: Compute autocorrelation of FT of raw SIM images +% k2fa: illumination frequency vector +% fS1aTnoisy: FT of raw SIM image +% OTFo: system OTF +% OPT: acronym for `OPTIMIZE'; to be set to 1 when this function is used +% for optimization, or else to 0 +% CCop: autocorrelation of fS1aTnoisy + +w = size(fS1aTnoisy,1); +wo = w/2; + +fS1aTnoisy = fS1aTnoisy.*(1-1*OTFo.^10); +fS1aT = fS1aTnoisy.*conj(OTFo); + +Kotf = OTFedgeF(OTFo); +DoubleMatSize = 0; +if ( 2*Kotf > wo ) + DoubleMatSize = 1; % 1 for doubling fourier domain size, 0 for keeping it unchanged +end + +if ( DoubleMatSize>0 ) + t = 2*w; + fS1aT_temp = zeros(t,t); + fS1aT_temp(wo+1:w+wo,wo+1:w+wo) = fS1aT; + clear fS1aT + fS1aT = fS1aT_temp; + clear fS1aT_temp +else + t = w; +end +to = t/2; +u = linspace(0,t-1,t); +v = linspace(0,t-1,t); +[U,V] = meshgrid(u,v); +S1aT = exp( -1i.*2*pi*( k2fa(2)/t.*(U-to)+k2fa(1)/t.*(V-to) ) ).*ifft2(fS1aT); +fS1aT0 = fft2( S1aT ); + +mA = sum(sum( fS1aT.*conj(fS1aT0) )); +mA = mA./sum(sum( fS1aT0.*conj(fS1aT0) )); + +if (OPT > 0) + CCop = -abs(mA); +else + CCop = mA; +end \ No newline at end of file diff --git a/SIMexpt/SIMo.m b/SIMexpt/SIMo.m new file mode 100644 index 0000000..a2aafd2 --- /dev/null +++ b/SIMexpt/SIMo.m @@ -0,0 +1,88 @@ +clear all +close all +clc + +%% Loading system OTF file +OTFo = double(imread('OTF.tif')); +OTFo = OTFpost(OTFo); + +%% Read Expt. Raw SIM Images +aa1 = imread('sim01z4.tif'); +aa = aa1(:,:,2); +bb = uint16(zeros(512,512,9)); +for ii=1:3 + for jj=1:3 + bb(1:512,1:512,(ii-1)*3+jj)=aa((ii-1)*512+1:ii*512,(jj-1)*512+1:jj*512,1); + end +end + +% separating the raw SIM images +S1aTnoisy = double( bb(:,:,1) ); +S2aTnoisy = double( bb(:,:,2) ); +S3aTnoisy = double( bb(:,:,3) ); +S1bTnoisy = double( bb(:,:,4) ); +S2bTnoisy = double( bb(:,:,5) ); +S3bTnoisy = double( bb(:,:,6) ); +S1cTnoisy = double( bb(:,:,7) ); +S2cTnoisy = double( bb(:,:,8) ); +S3cTnoisy = double( bb(:,:,9) ); +clear aa aa1 bb + +%% Intensity Normalization +[S1aTnoisy, S2aTnoisy, S3aTnoisy, ... + S1bTnoisy, S2bTnoisy, S3bTnoisy, ... + S1cTnoisy, S2cTnoisy, S3cTnoisy] = BgNormalization0(... + S1aTnoisy, S2aTnoisy, S3aTnoisy, ... + S1bTnoisy, S2bTnoisy, S3bTnoisy, ... + S1cTnoisy, S2cTnoisy, S3cTnoisy); + +%% Background subtraction +SE = strel('disk',20); +S1aTnoisy = S1aTnoisy - imopen(S1aTnoisy,SE); +S2aTnoisy = S2aTnoisy - imopen(S2aTnoisy,SE); +S3aTnoisy = S3aTnoisy - imopen(S3aTnoisy,SE); +S1bTnoisy = S1bTnoisy - imopen(S1bTnoisy,SE); +S2bTnoisy = S2bTnoisy - imopen(S2bTnoisy,SE); +S3bTnoisy = S3bTnoisy - imopen(S3bTnoisy,SE); +S1cTnoisy = S1cTnoisy - imopen(S1cTnoisy,SE); +S2cTnoisy = S2cTnoisy - imopen(S2cTnoisy,SE); +S3cTnoisy = S3cTnoisy - imopen(S3cTnoisy,SE); + + +%% obtaining the noisy estimates of three frequency components +[fAo,fAp,fAm,kA]... + = PCMseparateF(S1aTnoisy,S2aTnoisy,S3aTnoisy,OTFo); +[fBo,fBp,fBm,kB]... + = PCMseparateF(S1bTnoisy,S2bTnoisy,S3bTnoisy,OTFo); +[fCo,fCp,fCm,kC]... + = PCMseparateF(S1cTnoisy,S2cTnoisy,S3cTnoisy,OTFo); + +% averaging the central frequency components +fCent = (fAo + fBo + fCo)/3; + +% Object power parameters determination +OBJparaA = OBJpowerPara(fCent,OTFo); + +%% Wiener Filtering the noisy frequency components +[fAof,fApf,fAmf,Nao,Nap,Nam,Ma,DoubleMatSize]... + = PCMfilteringF(fAo,fAp,fAm,OTFo,OBJparaA,kA); +[fBof,fBpf,fBmf,Nbo,Nbp,Nbm,Mb,~]... + = PCMfilteringF(fBo,fBp,fBm,OTFo,OBJparaA,kB); +[fCof,fCpf,fCmf,Nco,Ncp,Ncm,Mc,~]... + = PCMfilteringF(fCo,fCp,fCm,OTFo,OBJparaA,kC); + + +%% doubling Fourier domain size if necessary +OTFo = OTFdoubling(OTFo,DoubleMatSize); + +%% merging all 9 frequency components using generalized Wiener Filter +[Fsum,Fperi,Fcent] = MergingHeptaletsF(fAof,fApf,fAmf,... + fBof,fBpf,fBmf,fCof,fCpf,fCmf,... + Ma,Mb,Mc,Nao,Nap,Nam,Nbo,Nbp,Nbm,... + Nco,Ncp,Ncm,kA,kB,kC,OBJparaA,OTFo); + + +% Plotting SIM results +SIMplot(Fsum,Fperi,Fcent,OTFo,kA,kB,kC,S1aTnoisy); + + diff --git a/SIMexpt/SIMplot.m b/SIMexpt/SIMplot.m new file mode 100644 index 0000000..9a5f42f --- /dev/null +++ b/SIMexpt/SIMplot.m @@ -0,0 +1,84 @@ +function [] = SIMplot(Fsum,Fperi,Fcent,OTFo,kA,kB,kC,S1aTnoisy) + +%% recontructed SIM images +Dcent = real( ifft2(fftshift(Fcent)) ); +Dsum = real( ifft2(fftshift(Fsum)) ); +Dperi = real( ifft2(fftshift(Fperi)) ); + +t = size(OTFo,1); +h = 1*30; +figure; +imshow(Dcent(h+1:t-h,h+1:t-h),[]) +title('Wiener-Filtered wide-field') +figure; +imshow(Dsum(h+1:t-h,h+1:t-h),[]) +title('SIM image') +figure; +imshow(Dperi(h+1:t-h,h+1:t-h),[]) +title('SIM image (using only off-center frequency components)') + +% appodizing the merged frequency components +Index = 0.4; +Kotf = OTFedgeF(OTFo); +[FsumA] = ApodizationFunction(Fsum,kA,kB,kC,Kotf,Index); +[FperiA] = ApodizationFunction(Fperi,kA,kB,kC,Kotf,Index); +DsumA = real( ifft2(fftshift(FsumA)) ); +DperiA = real( ifft2(fftshift(FperiA)) ); + +figure; +imshow(DsumA(h+1:t-h,h+1:t-h),[]) +title('appodized SIM image') +figure; +imshow(DperiA(h+1:t-h,h+1:t-h),[]) +title('appodized SIM image (using only off-center frequency components)') + + +%% Frequency Plots +fS1aTnoisy = fftshift(fft2(S1aTnoisy)); +w = size(OTFo,1); +wo = w/2; +w1 = size(fS1aTnoisy,1); +if ( w > w1 ) + fS1aTnoisy0 = zeros(w,w); + fS1aTnoisy0(wo-w1/2+1:wo+w1/2,wo-w1/2+1:wo+w1/2) = fS1aTnoisy; + clear fS1aTnoisy + fS1aTnoisy = fS1aTnoisy0; + clear fS1aTnoisy0; +end + + +p = 10; +minL1 = min(min( abs(fS1aTnoisy).^(1/p) )); +minL2 = min(min( abs(Fcent).^(1/p) )); +minL3 = min(min( abs(Fsum).^(1/p) )); +minL4 = min(min( abs(Fperi).^(1/p) )); +minL5 = min(min( abs(FsumA).^(1/p) )); +maxL1 = max(max( abs(fS1aTnoisy).^(1/p) )); +maxL2 = max(max( abs(Fcent).^(1/p) )); +maxL3 = max(max( abs(Fsum).^(1/p) )); +maxL4 = max(max( abs(Fperi).^(1/p) )); +maxL5 = max(max( abs(FsumA).^(1/p) )); +minL = min([minL1,minL2,minL3,minL4,minL5]); +maxL = max([maxL1,maxL2,maxL3,maxL4,maxL5]); + +figure; +imshow(abs(fS1aTnoisy).^(1/p),[minL maxL]) +title('fS1aTnoisy') + +figure; +imshow(abs(Fcent).^(1/p),[minL maxL]) +title('Weiner Filtered frequency') +figure; +imshow(abs(Fsum).^(1/p),[minL maxL]) +title('SIM frequency') +figure; +imshow(abs(Fperi).^(1/p),[minL maxL]) +title('SIM (off-center frequency components)') +figure; +imshow(abs(FsumA).^(1/p),[minL maxL]) +title('appodized SIM frequency') +figure; +imshow(abs(FperiA).^(1/p),[minL maxL]) +title('appodized SIM (off-center frequency components)') + + diff --git a/SIMexpt/SeparatedComponents2D.m b/SIMexpt/SeparatedComponents2D.m new file mode 100644 index 0000000..14d3880 --- /dev/null +++ b/SIMexpt/SeparatedComponents2D.m @@ -0,0 +1,22 @@ +function [FiSMao,FiSMap,FiSMam] = SeparatedComponents2D(... + phaseShift,phaseShift0,FcS1aT,FcS2aT,FcS3aT) +% Aim: Unmixing the frequency components of raw SIM images +% phaseShift,phaseShift0: illumination phase shifts +% FcS1aT,FcS2aT,FcS3aT: FT of raw SIM images +% FiSMao,FiSMap,FiSMam: unmixed frequency components of raw SIM images + +phaseShift1 = phaseShift(1,1); +phaseShift2 = phaseShift(2,1); +MF = 1.0; +%% Transformation Matrix +M = 0.5*[1 0.5*MF*exp(-1i*phaseShift0) 0.5*MF*exp(+1i*phaseShift0); + 1 0.5*MF*exp(-1i*phaseShift1) 0.5*MF*exp(+1i*phaseShift1); + 1 0.5*MF*exp(-1i*phaseShift2) 0.5*MF*exp(+1i*phaseShift2)]; + +%% Separting the components +%=========================================================== +Minv = inv(M); + +FiSMao = Minv(1,1)*FcS1aT + Minv(1,2)*FcS2aT + Minv(1,3)*FcS3aT; +FiSMap = Minv(2,1)*FcS1aT + Minv(2,2)*FcS2aT + Minv(2,3)*FcS3aT; +FiSMam = Minv(3,1)*FcS1aT + Minv(3,2)*FcS2aT + Minv(3,3)*FcS3aT; diff --git a/SIMexpt/TripletSNR0.m b/SIMexpt/TripletSNR0.m new file mode 100644 index 0000000..5b6069e --- /dev/null +++ b/SIMexpt/TripletSNR0.m @@ -0,0 +1,66 @@ +function [SIGao,SIGap2,SIGam2] = TripletSNR0(OBJpara,k2fa,OTFo,fDIp) + +% AIM: To obtain signal spectrums corresponding to central and off-center +% frequency components +% INPUT VARIABLES +% OBJpara: object power parameters +% k2fa: illumination frequency vector +% OTFo: system OTF +% fDIp: one of the off-center frequency component (utilized here only for +% visual verification of computation) +% OUTPUT VARIABLES +% SIGao: signal spectrum corresponding to central frequency component +% SIGap2,SIGam2: signal spectrums corresponding to off-center frequency +% components + +w = size(OTFo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Cv = (X-wo) + 1i*(Y-wo); +Ro = abs(Cv); + +% object spectrum parameters +Aobj = OBJpara(1); +Bobj = OBJpara(2); + +% object spectrums (default) +kv = k2fa(2) + 1i*k2fa(1); % vector along illumination direction +Rp = abs(Cv-kv); +Rm = abs(Cv+kv); +OBJo = Aobj*(Ro.^Bobj); +OBJp = Aobj*(Rp.^Bobj); +OBJm = Aobj*(Rm.^Bobj); + +OBJo(wo+1,wo+1) = 0.25*OBJo(wo+2,wo+1) + 0.25*OBJo(wo+1,wo+2)... + + 0.25*OBJo(wo+0,wo+1) + 0.25*OBJo(wo+1,wo+0); + +k3 = round(k2fa); +OBJp(wo+1+k3(1),wo+1+k3(2)) = 0.25*OBJp(wo+2+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+2+k3(2))... + + 0.25*OBJp(wo+0+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+0+k3(2)); +OBJm(wo+1-k3(1),wo+1-k3(2)) = 0.25*OBJm(wo+2-k3(1),wo+1-k3(2))... + + 0.25*OBJm(wo+1-k3(1),wo+2-k3(2))... + + 0.25*OBJm(wo+0-k3(1),wo+1-k3(2))... + + 0.25*OBJm(wo+1-k3(1),wo+0-k3(2)); + +% signal spectrums +SIGao = OBJo.*OTFo; +SIGap = OBJp.*OTFo; +SIGam = OBJm.*OTFo; + +SIGap2 = circshift(SIGap,-k3); +SIGam2 = circshift(SIGam,k3); + +%% for visual verification +%{ +pp = 3; +figure; +hold on +plot([0:w-1]-wo,log(abs(SIGap2(wo+pp,:))),'k--','LineWidth',3,'MarkerSize',6) +plot([0:w-1]-wo,log(abs(fDIp(wo+pp,:))),'mo-','LineWidth',2,'MarkerSize',6) +grid on +box on +%} \ No newline at end of file diff --git a/SIMexpt/WoFilterCenter.m b/SIMexpt/WoFilterCenter.m new file mode 100644 index 0000000..8299473 --- /dev/null +++ b/SIMexpt/WoFilterCenter.m @@ -0,0 +1,57 @@ +function [FiSMaof,NoisePower] = WoFilterCenter(FiSMao,OTFo,co,OBJpara,SFo) +% Aim: Wiener Filtering the central frequency component +% INPUT VARIABLES +% FiSMao: noisy central frequency component +% OTFo: system OTF +% co: Wiener filter constant [=1, for minimum RMS estimate] +% SFo: scaling factor (not significant here, so set to 1) +% OUTPUT VARIABLES +% FiSMaof: Wiener Filtered estimate of FiSMao +% NoisePower: avg. noise power in FiSMao + +w = size(FiSMao,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Ro = sqrt( (X-wo).^2 + (Y-wo).^2 ); + +OTFpower = OTFo.*conj(OTFo); + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +% frequency beyond which NoisePower estimate to be computed +NoiseFreq = Kotf + 20; + +% NoisePower determination +Zo = Ro>NoiseFreq; +nNoise = FiSMao.*Zo; +NoisePower = sum(sum( nNoise.*conj(nNoise) ))./sum(sum(Zo)); + +% Object Power determination +Aobj = OBJpara(1); +Bobj = OBJpara(2); +Ro(wo+1,wo+1) = 1; +OBJpower = Aobj*(Ro.^Bobj); +OBJpower = OBJpower.^2; + +%% Wiener Filtering +FiSMaof = FiSMao.*(SFo.*conj(OTFo)./NoisePower)./((SFo.^2).*OTFpower./NoisePower + co./OBJpower); + +%% for cross-checking filtered estimate visually +%{ +WFilter = (SFo.^2.*OTFpower./NoisePower)./((SFo.^2).*OTFpower./NoisePower + co./OBJpower); +FiSMao1 = FiSMaof.*OTFo; +pp = 3; +figure; +hold on +plot(x-wo,log(abs(FiSMaof(wo+pp,:))),'go--','LineWidth',2,'MarkerSize',6) +plot(x-wo,log(abs(FiSMao(wo+pp,:))),'o--','LineWidth',2,'MarkerSize',6) +plot(x-wo,log(abs(FiSMao1(wo+pp,:))),'r*--','LineWidth',2,'MarkerSize',4) +plot(x-wo,10*WFilter(wo+pp,:),'k*--','LineWidth',2,'MarkerSize',4) +title('WoFilter') +legend('FiSMaof','FiSMao','FiSMao1') +grid on +box on +%} \ No newline at end of file diff --git a/SIMexpt/WoFilterSideLobe.m b/SIMexpt/WoFilterSideLobe.m new file mode 100644 index 0000000..fb717c5 --- /dev/null +++ b/SIMexpt/WoFilterSideLobe.m @@ -0,0 +1,54 @@ +function [FiSMaof,NoisePower] = WoFilterSideLobe(FiSMao,OTFo,co,OBJsideP,SFo) +% Aim: Wiener Filtering the off-center frequency component +% INPUT VARIABLES +% FiSMao: noisy off-center frequency component +% OTFo: system OTF +% co: Wiener filter constant [=1, for minimum RMS estimate] +% OBJsideP: avg. object spectrum +% SFo: modulation factor +% OUTPUT VARIABLES +% FiSMaof: Wiener Filtered estimate of FiSMao +% NoisePower: avg. noise power in FiSMao + +w = size(FiSMao,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Ro = sqrt( (X-wo).^2 + (Y-wo).^2 ); + +OTFpower = OTFo.*conj(OTFo); + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +% frequency beyond which NoisePower estimate to be computed +NoiseFreq = Kotf + 20; + +% NoisePower determination +Zo = Ro>NoiseFreq; +nNoise = FiSMao.*Zo; +NoisePower = sum(sum( nNoise.*conj(nNoise) ))./sum(sum(Zo)); + +% Object Power determination +OBJpower = OBJsideP.^2; + +%% Wiener Filtering +FiSMaof = FiSMao.*(SFo.*conj(OTFo)./NoisePower)./((SFo.^2).*OTFpower./NoisePower + co./OBJpower); + +%% for cross-checking filtered estimate visually +%{ +WFilter = (SFo.^2.*OTFpower./NoisePower)./((SFo.^2).*OTFpower./NoisePower + co./OBJpower); +FiSMao1 = FiSMaof.*OTFo; +pp = 3; +figure; +hold on +plot(x-wo,log(abs(FiSMaof(wo+pp,:))),'go--','LineWidth',2,'MarkerSize',6) +plot(x-wo,log(abs(FiSMao(wo+pp,:))),'o--','LineWidth',2,'MarkerSize',6) +plot(x-wo,log(abs(FiSMao1(wo+pp,:))),'r*--','LineWidth',2,'MarkerSize',4) +plot(x-wo,10*WFilter(wo+pp,:),'k*--','LineWidth',2,'MarkerSize',4) 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zU*ghW5Ww7n-hriIb4{RfNYMBK(_lf&&as4{!5Cn92J1Ntf`)+X8qgjZP*?DKvC4{1 zg9BO!0rdk*+i4G=z@B$-T__Z6|KJc{#sb0$O9R;FmB-S0BA_; z^aK}EK&}As1=9e}4(cyZ7pxxuFM$4n>SAdiy@Vn#z_)lH46rn877U*ks2~_Wpd1S9 zx3Dy@?F49GTLK6vFqAvq0a#BE&wy+I7X$C$1p%^uKzo3R1<3}09|W7;!tV#xaO|M% zzz^FVWJg^%94s$DIl-Op5QKwb5P&}*y#nqBFcSuk2MP*B2!h5Jpb28v1M&I+*f5aI z26Avf*aVVOz-sKYr+_8d(GMsZU=jQdG_a``Ov9kT_7n)rwo=V_{J{XX4{i^J0HOg< zdw`4D5l_NlD6r0;fSmG_)%K=}Vf#n_n1baL9Ln5$Cq8gQUG z*wz8DC}26j?E%TS9d%)V0o+jzo9D#G4+)3k`dVj4BVcvg5xdH+YG>!n2EYv@%jIm% z?AU round(0.5*Kotf); +Z1 = X > wo; + +FiSMap = FiSMap.*Z0.*Z1; +dumY = max( FiSMap,[],1 ); +[dummy Iy] = max(dumY); +dumX = max( FiSMap,[],2 ); +[dummy Ix] = max(dumX); + +maxK2 = [Ix-(wo+1) Iy-(wo+1)]; + + diff --git a/SIMbasic/IlluminationFreqF.m b/SIMbasic/IlluminationFreqF.m new file mode 100644 index 0000000..8dd5ec4 --- /dev/null +++ b/SIMbasic/IlluminationFreqF.m @@ -0,0 +1,38 @@ +function [k2fa] = IlluminationFreqF(S1aTnoisy,OTFo) +% AIM: illumination frequency vector determination +% INPUT VARIABLES +% S1aTnoisy: raw SIM image +% OTFo: system OTF +% OUTPUT VARIABLE +% k2fa: illumination frequency vector + +w = size(OTFo,1); +wo = w/2; + +% computing PSFe for edge tapering SIM images +PSFd = real(fftshift( ifft2(fftshift(OTFo.^10)) )); +PSFd = PSFd/max(max(PSFd)); +PSFd = PSFd/sum(sum(PSFd)); +h = 30; +PSFe = PSFd(wo-h+1:wo+h,wo-h+1:wo+h); + +% edge tapering raw SIM image +S1aTnoisy_et = edgetaper(S1aTnoisy,PSFe); +fS1aTnoisy_et = fftshift(fft2(S1aTnoisy_et)); + +% OTF cut-off freq +Kotf = OTFedgeF(OTFo); + +% Approx illumination frequency vector +[k2fa,~,~] = ApproxFreqDuplex(fS1aTnoisy_et,Kotf); + +fS1aTnoisy = fftshift(fft2(S1aTnoisy)); +% illumination frequency vector determination by optimizing +% autocorrelation of fS1aTnoisy +OPT = 1; +PhaseKai2opt0 = @(k2fa0)PhaseKai2opt(k2fa0,fS1aTnoisy,OTFo,OPT); +options = optimset('LargeScale','off','Algorithm',... + 'active-set','MaxFunEvals',500,'MaxIter',500,'Display','notify'); +k2fa0 = k2fa; +[k2fa,fval] = fminsearch(PhaseKai2opt0,k2fa0,options); +% k2a = sqrt(k2fa*k2fa') diff --git a/SIMbasic/IlluminationPhaseF.m b/SIMbasic/IlluminationPhaseF.m new file mode 100644 index 0000000..2898568 --- /dev/null +++ b/SIMbasic/IlluminationPhaseF.m @@ -0,0 +1,14 @@ +function [phaseA1] = IlluminationPhaseF(S1aTnoisy,k2fa) +% AIM: illumination phase shift determination +% INPUT VARIABLES +% S1aTnoisy: raw SIM image +% k2fa: illumination frequency vector +% OUTPUT VARIABLE +% phaseA1: illumination phase shift determined + +PatternPhaseOpt0 = @(phaseA0)PatternPhaseOpt(phaseA0,S1aTnoisy,k2fa); +options = optimset('LargeScale','off','Algorithm',... + 'active-set','MaxFunEvals',500,'MaxIter',500,'Display','notify'); +phaseA0 = 0; +[phaseA1,fval] = fminsearch(PatternPhaseOpt0,phaseA0,options); +% phaseA1*180/pi \ No newline at end of file diff --git a/SIMbasic/MergingHeptaletsF.m b/SIMbasic/MergingHeptaletsF.m new file mode 100644 index 0000000..19a98f6 --- /dev/null +++ b/SIMbasic/MergingHeptaletsF.m @@ -0,0 +1,68 @@ +function [Fsum,Fperi,Fcent] = MergingHeptaletsF(fDIo,fDIp,fDIm,fDBo,fDBp,fDBm,... + fDCo,fDCp,fDCm,Ma,Mb,Mc,npDIo,npDIp,npDIm,... + npDBo,npDBp,npDBm,npDCo,npDCp,npDCm,k2fa,k2fb,k2fc,OBJpara,OTFo) + +% AIM: To merge all 9 frequency components into one using generalized +% Wiener Filter +% INPUT VARIABLES +% [fDIo fDIp fDIm +% fDBo fDBp fDBm +% fDCo fDCp fDCm]: nine frequency components +% Ma,Mb,Mc: modulation factors for the three illumination orientations +% [npDIo npDIp npDIm +% npDBo npDBp npDBm +% npDCo,npDCp,npDCm]: noise powers corresponding to nine frequency +% components +% k2fa,k2fb,k2fc: illumination frequency vectors for the three +% illumination orientations +% OBJpara: Object spectrum parameters +% OTFo: system OTF +% OUTPUT VARIABLES +% Fsum: all nine frequency components merged into one using +% generalised Wiener Filter +% Fperi: six off-center frequency components merged into one using +% generalised Wiener Filter +% Fcent: averaged of the three central frequency components + + +% obtain signal spectrums corresponding to central and off-center +% frequency components +[SIGao,SIGam2,SIGap2] = TripletSNR0(OBJpara,k2fa,OTFo,fDIm); +[SIGbo,SIGbm2,SIGbp2] = TripletSNR0(OBJpara,k2fb,OTFo,fDBm); +[SIGco,SIGcm2,SIGcp2] = TripletSNR0(OBJpara,k2fc,OTFo,fDCm); + +SIGap2 = Ma*SIGap2; +SIGam2 = Ma*SIGam2; +SIGbp2 = Mb*SIGbp2; +SIGbm2 = Mb*SIGbm2; +SIGcp2 = Mc*SIGcp2; +SIGcm2 = Mc*SIGcm2; + +%% Generalized Wiener-Filter computation +SNRao = SIGao.*conj(SIGao)./npDIo; +SNRap = SIGap2.*conj(SIGap2)./npDIp; +SNRam = SIGam2.*conj(SIGam2)./npDIm; + +SNRbo = SIGbo.*conj(SIGbo)./npDBo; +SNRbp = SIGbp2.*conj(SIGbp2)./npDBp; +SNRbm = SIGbm2.*conj(SIGbm2)./npDBm; + +SNRco = SIGco.*conj(SIGco)./npDCo; +SNRcp = SIGcp2.*conj(SIGcp2)./npDCp; +SNRcm = SIGcm2.*conj(SIGcm2)./npDCm; + +ComDeno = 0.01 + ( SNRao + SNRap + SNRam + SNRbo + SNRbp + SNRbm + SNRco + SNRcp + SNRcm ); +Fsum = fDIo.*SNRao + fDIp.*SNRap + fDIm.*SNRam... + + fDBo.*SNRbo + fDBp.*SNRbp + fDBm.*SNRbm... + + fDCo.*SNRco + fDCp.*SNRcp + fDCm.*SNRcm; +Fsum = Fsum./ComDeno; + +ComPeri = 0.01 + ( SNRap + SNRam + SNRbp + SNRbm + SNRcp + SNRcm ); +Fperi = fDIp.*SNRap + fDIm.*SNRam + fDBp.*SNRbp + fDBm.*SNRbm... + + fDCp.*SNRcp + fDCm.*SNRcm; +Fperi = Fperi./ComPeri; + +% averaged central frequency component +Fcent = (fDIo+fDBo+fDCo)/3; + + diff --git a/SIMbasic/ModulationFactor.m b/SIMbasic/ModulationFactor.m new file mode 100644 index 0000000..2ac2dda --- /dev/null +++ b/SIMbasic/ModulationFactor.m @@ -0,0 +1,86 @@ +function Mm = ModulationFactor(fDp,k1a,OBJparaA,OTFo) +% AIM: Determination of modulation factor +% INPUT VARIABLES +% fDp: off-center frequency component +% k1a: illumination frequency vector +% OBJparaA: Object power parameters +% OTFo: system OTF +% OUTPUT VARIABLE +% Mm: modulation factor + +w = size(OTFo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Cv = (X-wo) + 1i*(Y-wo); +Ro = abs(Cv); + +% magnitude of illumination vector +k2 = sqrt(k1a*k1a'); + +% vector along illumination direction +kv = k1a(2) + 1i*k1a(1); +Rp = abs(Cv+kv); + +% Object power parameters +Aobj = OBJparaA(1); +Bobj = OBJparaA(2); + +% Object spectrum +OBJp = Aobj*(Rp+0).^Bobj; + +% illumination vector rounded to nearest pixel +k3 = -round(k1a); + +OBJp(wo+1+k3(1),wo+1+k3(2)) = 0.25*OBJp(wo+2+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+2+k3(2))... + + 0.25*OBJp(wo+0+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+0+k3(2)); + +% signal spectrum +SIGap = OBJp.*OTFo; + +% figure; +% mesh(log(abs(OBJp))) +% figure; +% mesh(log(abs(fDp))) + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +% frequency beyond which NoisePower estimate to be computed +NoiseFreq = Kotf + 20; + +% NoisePower determination +Zo = Ro>NoiseFreq; +nNoise = fDp.*Zo; +NoisePower = sum(sum( nNoise.*conj(nNoise) ))./sum(sum(Zo)); + +% Noise free object power computation +Fpower = fDp.*conj(fDp) - NoisePower; +fDp = sqrt(abs(Fpower)); + +% frequency range over which signal power matching is done to estimate +% modulation factor +Zmask = (Ro > 0.2*k2).*(Ro < 0.8*k2).*(Rp > 0.2*k2); + +% least square approximation for modulation factor +Mm = sum(sum(SIGap.*abs(fDp).*Zmask)); +Mm = Mm./sum(sum(SIGap.^2.*Zmask)) + +%% for visual verification +%{ +pp = 3; +figure; +hold on +plot(x-wo,log(abs(fDp(wo+pp,:))),'o-','LineWidth',2,'MarkerSize',6) +plot(x-wo,log(abs(SIGap(wo+pp,:))),'go--','LineWidth',2,'MarkerSize',4) +plot(x-wo,log(abs(Mm*SIGap(wo+pp,:))),'r*--','LineWidth',2,'MarkerSize',4) +grid on +box on +kk +%} + + + diff --git a/SIMbasic/OBJparaOpt.m b/SIMbasic/OBJparaOpt.m new file mode 100644 index 0000000..8acbbbb --- /dev/null +++ b/SIMbasic/OBJparaOpt.m @@ -0,0 +1,47 @@ +function Esum = OBJparaOpt(OBJpara0,fDIoTnoisy,OTFo) +% AIM: Determined Sum of Squared Errors (SSE) between `actual signal power' and +% `approximated signal power' +% INPUT VARIABLES +% OBJpara0: [Aobj Bobj], Object power parameters +% fDIoTnoisy: FT of central frequency component +% OTFo: system OTF +% OUTPUT VARIABLE +% Esum: SSE between `actual signal spectrum' and `approximated signal spectrum' + +w = size(OTFo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Cv = (X-wo) + 1i*(Y-wo); +Ro = abs(Cv); +Ro(wo+1,wo+1) = 1; % to avoid nan + +% approximated signal power calculation +Aobj = OBJpara0(1); +Bobj = OBJpara0(2); +OBJpower = Aobj*(Ro.^Bobj); +SIGpower = OBJpower.*OTFo; + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +% range of frequency over which SSE is computed +Zloop = (Ro<0.75*Kotf).*(Ro>0.25*Kotf); + +% frequency beyond which NoisePower estimate to be computed +NoiseFreq = Kotf + 20; + +% NoisePower determination +Zo = Ro>NoiseFreq; +nNoise = fDIoTnoisy.*Zo; +NoisePower = sum(sum( nNoise.*conj(nNoise) ))./sum(sum(Zo)); + +% Noise free object power computation +Fpower = fDIoTnoisy.*conj(fDIoTnoisy) - NoisePower; +fDIoTnoisy = sqrt(abs(Fpower)); + +% SSE computation +Error = fDIoTnoisy - SIGpower; +Esum = sum(sum((Error.^2./Ro).*Zloop)); + diff --git a/SIMbasic/OBJpowerPara.m b/SIMbasic/OBJpowerPara.m new file mode 100644 index 0000000..9ef86ce --- /dev/null +++ b/SIMbasic/OBJpowerPara.m @@ -0,0 +1,48 @@ +function OBJparaA = OBJpowerPara(fDIoTnoisy,OTFo) +% AIM: determination of object power parameters Aobj and Bobj +% INPUT VARIABLES +% fDIoTnoisy: FT of central frequency component +% OTFo: system OTFo +% OUTPUT VARIABLES +% OBJparaA: [Aobj Bobj] + +w = size(OTFo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Cv = (X-wo) + 1i*(Y-wo); +Ro = abs(Cv); + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +%% object power parameters through optimization +OBJparaOpt0 = @(OBJpara0)OBJparaOpt(OBJpara0,fDIoTnoisy,OTFo); +options = optimset('LargeScale','off','Algorithm',... + 'active-set','MaxFunEvals',500,'MaxIter',500,'Display','notify'); + +% obtaining crude initial guesses for Aobj and Bobj +Zm = (Ro>0.3*Kotf).*(Ro<0.4*Kotf); +Aobj = sum(sum(abs(fDIoTnoisy.*Zm)))./sum(sum(Zm)); +Bobj = -0.5; +OBJpara0 = [Aobj Bobj]; + +% optimization step +[OBJparaA,fval] = fminsearch(OBJparaOpt0,OBJpara0,options); + +%% plot for cross-checking the result +%{ +Aobj = OBJparaA(1); +Bobj = OBJparaA(2); +OBJo = Aobj*(Ro.^Bobj); +SIGp = OBJo.*OTFo; +pp = 3; +figure; +hold on +plot([0:w-1]-wo,log(abs(fDIoTnoisy(wo+pp,:))),'k--','LineWidth',3,'MarkerSize',6) +plot([0:w-1]-wo,log(abs(SIGp(wo+pp,:))),'mo-','LineWidth',2,'MarkerSize',6) +legend('acutal signal power','avg. signal power') +grid on +box on +%} \ No newline at end of file diff --git a/SIMbasic/OTFdoubling.m b/SIMbasic/OTFdoubling.m new file mode 100644 index 0000000..58aaa6e --- /dev/null +++ b/SIMbasic/OTFdoubling.m @@ -0,0 +1,17 @@ +function OTF2 = OTFdoubling(OTFo,DoubleMatSize) + +%% embeds OTFo in doubled range of frequencies + +w = size(OTFo,1); +wo = w/2; +if ( DoubleMatSize>0 ) + t = 2*w; + u = linspace(0,t-1,t); + v = linspace(0,t-1,t); + OTF2 = zeros(2*w,2*w); + OTF2(wo+1:w+wo,wo+1:w+wo) = OTFo; + clear OTFo +else + OTF2 = OTFo; + clear OTFo +end \ No newline at end of file diff --git a/SIMbasic/OTFedgeF.m b/SIMbasic/OTFedgeF.m new file mode 100644 index 0000000..e4d6a7f --- /dev/null +++ b/SIMbasic/OTFedgeF.m @@ -0,0 +1,13 @@ +function Kotf = OTFedgeF(OTFo) + +w = size(OTFo,1); +wo = w/2; + +OTF1 = OTFo(wo+1,:); +OTFmax = max(max(abs(OTFo))); +OTFtruncate = 0.01; +i = 1; +while ( abs(OTF1(1,i)) Kotf; \ No newline at end of file diff --git a/SIMbasic/PCMfilteringF.m b/SIMbasic/PCMfilteringF.m new file mode 100644 index 0000000..3a04408 --- /dev/null +++ b/SIMbasic/PCMfilteringF.m @@ -0,0 +1,143 @@ +function [fDof,fDp2,fDm2,npDo,npDp,npDm,Mm,DoubleMatSize]... + = PCMfilteringF(fDo,fDp,fDm,OTFo,OBJparaA,kA) + +% AIM: obtaining Wiener Filtered estimates of noisy frequency components +% INPUT VARIABLES +% fDo,fDp,fDm: noisy estimates of separated frequency components +% OTFo: system OTF +% OBJparaA: object power parameters +% kA: illumination vector +% OUTPUT VARIABLES +% fDof,fDp2,fDm2: Wiener Filtered estimates of fDo,fDp,fDm +% npDo,npDp,npDm: avg. noise power in fDo,fDp,fDm +% Mm: illumination modulation factor +% DoubleMatSize: parameter for doubling FT size if necessary + +w = size(OTFo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Cv = (X-wo) + 1i*(Y-wo); +Ro = abs(Cv); + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +% object power parameters +Aobj = OBJparaA(1); +Bobj = OBJparaA(2); + +% Wiener Filtering central frequency component +SFo = 1; +co = 1.0; +[fDof,npDo] = WoFilterCenter(fDo,OTFo,co,OBJparaA,SFo); + +% modulation factor determination +Mm = ModulationFactor(fDp,kA,OBJparaA,OTFo); + +%% Duplex power (default) +kv = kA(2) + 1i*kA(1); % vector along illumination direction +Rp = abs(Cv-kv); +Rm = abs(Cv+kv); +OBJp = Aobj*(Rp.^Bobj); +OBJm = Aobj*(Rm.^Bobj); +k3 = round(kA); +OBJp(wo+1+k3(1),wo+1+k3(2)) = 0.25*OBJp(wo+2+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+2+k3(2))... + + 0.25*OBJp(wo+0+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+0+k3(2)); +OBJm(wo+1-k3(1),wo+1-k3(2)) = 0.25*OBJm(wo+2-k3(1),wo+1-k3(2))... + + 0.25*OBJm(wo+1-k3(1),wo+2-k3(2))... + + 0.25*OBJm(wo+0-k3(1),wo+1-k3(2))... + + 0.25*OBJm(wo+1-k3(1),wo+0-k3(2)); + +% Filtering side lobes (off-center frequency components) +SFo = Mm; +[fDpf,npDp] = WoFilterSideLobe(fDp,OTFo,co,OBJm,SFo); +[fDmf,npDm] = WoFilterSideLobe(fDm,OTFo,co,OBJp,SFo); + +%% doubling Fourier domain size if necessary +DoubleMatSize = 0; +if ( 2*Kotf > wo ) + DoubleMatSize = 1; % 1 for doubling fourier domain size, 0 for keeping it unchanged +end +if ( DoubleMatSize>0 ) + t = 2*w; + to = t/2; + u = linspace(0,t-1,t); + v = linspace(0,t-1,t); + [U,V] = meshgrid(u,v); + fDoTemp = zeros(2*w,2*w); + fDpTemp = zeros(2*w,2*w); + fDmTemp = zeros(2*w,2*w); + OTFtemp = zeros(2*w,2*w); + fDoTemp(wo+1:w+wo,wo+1:w+wo) = fDof; + fDpTemp(wo+1:w+wo,wo+1:w+wo) = fDpf; + fDmTemp(wo+1:w+wo,wo+1:w+wo) = fDmf; + OTFtemp(wo+1:w+wo,wo+1:w+wo) = OTFo; + clear fDof fDpf fDmf OTFo w wo x y X Y + fDof = fDoTemp; + fDpf = fDpTemp; + fDmf = fDmTemp; + OTFo = OTFtemp; + clear fDoTemp fDpTemp fDmTemp OTFtemp +else + t = w; + to = t/2; + u = linspace(0,t-1,t); + v = linspace(0,t-1,t); + [U,V] = meshgrid(u,v); +end + +% Shifting the off-center frequency components to their correct location +fDp1 = fft2(ifft2(fDpf).*exp( +1i.*2*pi*(kA(2)/t.*(U-to) + kA(1)/t.*(V-to)) )); +fDm1 = fft2(ifft2(fDmf).*exp( -1i.*2*pi*(kA(2)/t.*(U-to) + kA(1)/t.*(V-to)) )); + +%% Shift induced phase error correction +Cv = (U-to) + 1i*(V-to); +Ro = abs(Cv); +Rp = abs(Cv-kv); +k2 = sqrt(kA*kA'); + +% frequency range over which corrective phase is determined +Zmask = (Ro < 0.8*k2).*(Rp < 0.8*k2); + +% corrective phase +Angle0 = angle( sum(sum( fDof.*conj(fDp1).*Zmask )) ); + +% phase correction +fDp2 = exp(+1i*Angle0).*fDp1; +fDm2 = exp(-1i*Angle0).*fDm1; + +%% for visual verification +%{ +pp = 3; +figure; +hold on +plot(u-to,angle(fDof(to+pp,:)).*180/pi,'o-','LineWidth',2,'MarkerSize',8) +plot(u-to,angle(fDp1(to+pp,:)).*180/pi,'ro-','LineWidth',2,'MarkerSize',8) +plot(u-to,angle(fDp2(to+pp,:)).*180/pi,'go--','LineWidth',2,'MarkerSize',6) +grid on +box on +figure; +hold on +plot3(u-to,real(fDof(to+1,:)),imag(fDof(to+1,:)),'o-','LineWidth',2,'MarkerSize',8) +plot3(u-to,real(fDp1(to+1,:)),imag(fDp1(to+1,:)),'ro-','LineWidth',2,'MarkerSize',8) +plot3(u-to,real(fDp2(to+1,:)),imag(fDp2(to+1,:)),'go--','LineWidth',2,'MarkerSize',6) +grid on +box on + +ff1 = fDof.*conj(fDp1); +ff2 = fDof.*conj(fDp2); +figure; +hold on +plot(u-to,angle(ff1(to+pp,:)).*180/pi,'ro-','LineWidth',2,'MarkerSize',8) +plot(u-to,angle(ff2(to+pp,:)).*180/pi,'go--','LineWidth',2,'MarkerSize',6) +grid on +box on +%} + + + + diff --git a/SIMbasic/PCMseparateF.m b/SIMbasic/PCMseparateF.m new file mode 100644 index 0000000..d6b12d8 --- /dev/null +++ b/SIMbasic/PCMseparateF.m @@ -0,0 +1,64 @@ +function [fDo,fDp,fDm,kA]... + = PCMseparateF(S1aTnoisy,S2aTnoisy,S3aTnoisy,OTFo) +% AIM: obtaining the noisy estimates of three frequency components +% INPUT VARIABLES +% S1aTnoisy,S2aTnoisy,S3aTnoisy: 3 raw SIM images with identical +% illumination pattern orientation +% but different phase shifts +% OTFo: system OTF +% OUTPUT VARIABLES +% fDo,fDp,fDm: noisy estimates of separated frequency components +% kA: (averaged) illumination frequency vector + + +w = size(S1aTnoisy,1); +wo = w/2; + +%% Determination of illumination frequency vectors +[k1a] = IlluminationFreqF(S1aTnoisy,OTFo); +[k2a] = IlluminationFreqF(S2aTnoisy,OTFo); +[k3a] = IlluminationFreqF(S3aTnoisy,OTFo); + +% mean illumination frequency vector +kA = (k1a + k2a + k3a)/3; + +%% determination of illumination phase shifts +[phase1A] = IlluminationPhaseF(S1aTnoisy,kA); +[phase2A] = IlluminationPhaseF(S2aTnoisy,kA); +[phase3A] = IlluminationPhaseF(S3aTnoisy,kA); + +% for display in command window +phaseA = [phase1A; phase2A; phase3A]; +phaseA*180/pi + +% computing PSFe for edge tapering SIM images +PSFd = real(fftshift( ifft2(fftshift(OTFo.^3)) )); +PSFd = PSFd/max(max(PSFd)); +PSFd = PSFd/sum(sum(PSFd)); +h = 30; +PSFe = PSFd(wo-h+1:wo+h,wo-h+1:wo+h); + +% edge tapering raw SIM images +S1aTnoisy = edgetaper(S1aTnoisy,PSFe); +S2aTnoisy = edgetaper(S2aTnoisy,PSFe); +S3aTnoisy = edgetaper(S3aTnoisy,PSFe); + +fS1aTnoisy = fftshift(fft2(S1aTnoisy)); +fS2aTnoisy = fftshift(fft2(S2aTnoisy)); +fS3aTnoisy = fftshift(fft2(S3aTnoisy)); + +%% Separating the three frequency components +phaseShift0 = phase1A; +phaseShift = [phase2A; phase3A]; +[fDo,fDp,fDm] = SeparatedComponents2D(... + phaseShift,phaseShift0,fS1aTnoisy,fS2aTnoisy,fS3aTnoisy); + +%% for visual verification +%{ +figure; +mesh(log(abs(fDo))) +figure; +mesh(log(abs(fDp))) +figure; +mesh(log(abs(fDm))) +%} diff --git a/SIMbasic/PatternPhaseOpt.m b/SIMbasic/PatternPhaseOpt.m new file mode 100644 index 0000000..022539a --- /dev/null +++ b/SIMbasic/PatternPhaseOpt.m @@ -0,0 +1,12 @@ +function CCop = PatternPhaseOpt(phaseA,S1aTnoisy,k2fa) + +w = size(S1aTnoisy,1); +wo = w/2; + +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); + +sAo = cos( 2*pi*(k2fa(2).*(X-wo)+k2fa(1).*(Y-wo))./w + phaseA ); +S1aTnoisy = S1aTnoisy - mean2(S1aTnoisy); +CCop = -sum(sum(S1aTnoisy.*sAo)); \ No newline at end of file diff --git a/SIMbasic/PhaseKai2opt.m b/SIMbasic/PhaseKai2opt.m new file mode 100644 index 0000000..bb7ec1f --- /dev/null +++ b/SIMbasic/PhaseKai2opt.m @@ -0,0 +1,46 @@ +function [CCop] = PhaseKai2opt(k2fa,fS1aTnoisy,OTFo,OPT) +% Aim: Compute autocorrelation of FT of raw SIM images +% k2fa: illumination frequency vector +% fS1aTnoisy: FT of raw SIM image +% OTFo: system OTF +% OPT: acronym for `OPTIMIZE'; to be set to 1 when this function is used +% for optimization, or else to 0 +% CCop: autocorrelation of fS1aTnoisy + +w = size(fS1aTnoisy,1); +wo = w/2; + +fS1aTnoisy = fS1aTnoisy.*(1-1*OTFo.^10); +fS1aT = fS1aTnoisy.*conj(OTFo); + +Kotf = OTFedgeF(OTFo); +DoubleMatSize = 0; +if ( 2*Kotf > wo ) + DoubleMatSize = 1; % 1 for doubling fourier domain size, 0 for keeping it unchanged +end + +if ( DoubleMatSize>0 ) + t = 2*w; + fS1aT_temp = zeros(t,t); + fS1aT_temp(wo+1:w+wo,wo+1:w+wo) = fS1aT; + clear fS1aT + fS1aT = fS1aT_temp; + clear fS1aT_temp +else + t = w; +end +to = t/2; +u = linspace(0,t-1,t); +v = linspace(0,t-1,t); +[U,V] = meshgrid(u,v); +S1aT = exp( -1i.*2*pi*( k2fa(2)/t.*(U-to)+k2fa(1)/t.*(V-to) ) ).*ifft2(fS1aT); +fS1aT0 = fft2( S1aT ); + +mA = sum(sum( fS1aT.*conj(fS1aT0) )); +mA = mA./sum(sum( fS1aT0.*conj(fS1aT0) )); + +if (OPT > 0) + CCop = -abs(mA); +else + CCop = mA; +end \ No newline at end of file diff --git a/SIMbasic/PsfOtf.m b/SIMbasic/PsfOtf.m new file mode 100644 index 0000000..0120d1c --- /dev/null +++ b/SIMbasic/PsfOtf.m @@ -0,0 +1,34 @@ +function [yy0,OTF2dc] = PsfOtf(w,scale) + +% AIM: To generate PSF and OTF using Bessel function +% INPUT VARIABLES +% w: image size +% scale: a parameter used to adjust PSF/OTF width +% OUTPUT VRAIBLES +% yyo: system PSF +% OTF2dc: system OTF + +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); + +%% Generation of the PSF with Besselj. +% scale = 0.3; +R=sqrt(min(X,abs(X-w)).^2+min(Y,abs(Y-w)).^2); +yy=abs(2*besselj(1,scale*R+eps,1)./(scale*R+eps)).^2; %0.5 is introduced to make PSF wider +yy0 = fftshift(yy); +% figure; +% mesh(X,Y,yy0) +% figure; +% imshow(yy0,[]) +% axis square + +%Generate 2D OTF. +OTF2d=fft2(yy); +OTF2dmax = max(max(abs(OTF2d))); +OTF2d = OTF2d./OTF2dmax; +OTF2dc = abs(fftshift(OTF2d)); +% figure; +% mesh(abs(OTF2dc)) +% title('OTF of the system') +% axis square \ No newline at end of file diff --git a/SIMbasic/SIMimagesF.m b/SIMbasic/SIMimagesF.m new file mode 100644 index 0000000..6b93dba --- /dev/null +++ b/SIMbasic/SIMimagesF.m @@ -0,0 +1,282 @@ +function [S1aTnoisy S2aTnoisy S3aTnoisy ... + S1bTnoisy S2bTnoisy S3bTnoisy ... + S1cTnoisy S2cTnoisy S3cTnoisy ... + DIoTnoisy DIoT] = SIMimagesF(k2,... + DIo,PSFo,OTFo,ModFac,NoiseLevel,UsePSF) + +% AIM: to generate raw sim images +% INPUT VARIABLES +% k2: illumination frequency +% DIo: specimen image +% PSFo: system PSF +% OTFo: system OTF +% UsePSF: 1 (to blur SIM images by convloving with PSF) +% 0 (to blur SIM images by truncating its fourier content beyond OTF) +% NoiseLevel: percentage noise level for generating gaussian noise +% OUTPUT VARIABLES +% [S1aTnoisy S2aTnoisy S3aTnoisy +% S1bTnoisy S2bTnoisy S3bTnoisy +% S1cTnoisy S2cTnoisy S3cTnoisy]: nine raw sim images +% DIoTnoisy: noisy wide field image +% DIoT: noise-free wide field image + +w = size(DIo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); + +%% illunination phase shifts along the three directions +p0Ao = 0*pi/3; +p0Ap = 2*pi/3; +p0Am = 4*pi/3; +p0Bo = 0*pi/3; +p0Bp = 2*pi/3; +p0Bm = 4*pi/3; +p0Co = 0*pi/3; +p0Cp = 2*pi/3; +p0Cm = 4*pi/3; + +%% Illuminating patterns +alpha = 0*pi/6; +% orientation direction of illumination patterns +thetaA = 0*pi/3 + alpha; +thetaB = 1*pi/3 + alpha; +thetaC = 2*pi/3 + alpha; +% illumination frequency vectors +k2a = (k2/w).*[cos(thetaA) sin(thetaA)]; +k2b = (k2/w).*[cos(thetaB) sin(thetaB)]; +k2c = (k2/w).*[cos(thetaC) sin(thetaC)]; +% ------------------------------------------------------- +% mean illumination intensity +mA = 0.5; +mB = 0.5; +mC = 0.5; +% amplitude of illumination intensity above mean +aA = 0.5*ModFac; +aB = 0.5*ModFac; +aC = 0.5*ModFac; + +% random phase shift errors +NN = 1*(0.5-rand(9,1))*pi/18; + +% illunination phase shifts with random errors +psAo = p0Ao + NN(1,1); +psAp = p0Ap + NN(2,1); +psAm = p0Am + NN(3,1); +psBo = p0Bo + NN(4,1); +psBp = p0Bp + NN(5,1); +psBm = p0Bm + NN(6,1); +psCo = p0Co + NN(7,1); +psCp = p0Cp + NN(8,1); +psCm = p0Cm + NN(9,1); + +% illunination patterns +sAo = mA + aA*cos(2*pi*(k2a(1,1).*(X-wo)+k2a(1,2).*(Y-wo))+psAo); % illuminated signal (0 phase) +sAp = mA + aA*cos(2*pi*(k2a(1,1).*(X-wo)+k2a(1,2).*(Y-wo))+psAp); % illuminated signal (+ phase) +sAm = mA + aA*cos(2*pi*(k2a(1,1).*(X-wo)+k2a(1,2).*(Y-wo))+psAm); % illuminated signal (- phase) +sBo = mB + aB*cos(2*pi*(k2b(1,1).*(X-wo)+k2b(1,2).*(Y-wo))+psBo); % illuminated signal (0 phase) +sBp = mB + aB*cos(2*pi*(k2b(1,1).*(X-wo)+k2b(1,2).*(Y-wo))+psBp); % illuminated signal (+ phase) +sBm = mB + aB*cos(2*pi*(k2b(1,1).*(X-wo)+k2b(1,2).*(Y-wo))+psBm); % illuminated signal (- phase) +sCo = mC + aC*cos(2*pi*(k2c(1,1).*(X-wo)+k2c(1,2).*(Y-wo))+psCo); % illuminated signal (0 phase) +sCp = mC + aC*cos(2*pi*(k2c(1,1).*(X-wo)+k2c(1,2).*(Y-wo))+psCp); % illuminated signal (+ phase) +sCm = mC + aC*cos(2*pi*(k2c(1,1).*(X-wo)+k2c(1,2).*(Y-wo))+psCm); % illuminated signal (- phase) + +%{ +fftemp = fftshift(fft2(sAo)); +figure; +hold on +plot(x-wo,abs(OTFo(wo+1,:)),'--','LineWidth',2,'MarkerSize',6) +plot(x-wo,0.5*abs(fftemp(wo+1,:))./max(max(abs(fftemp))),'r--','LineWidth',2,'MarkerSize',6) +legend('OTFo','illumination spectrum') +grid on +box on +%} + +% figure; +% imshow(sAo,[ ]) +% kk + +%% superposed Objects +s1a = DIo.*sAo; % superposed signal (0 phase) +s2a = DIo.*sAp; % superposed signal (+ phase) +s3a = DIo.*sAm; % superposed signal (- phase) +s1b = DIo.*sBo; +s2b = DIo.*sBp; +s3b = DIo.*sBm; +s1c = DIo.*sCo; +s2c = DIo.*sCp; +s3c = DIo.*sCm; +%{ +figure; +subplot(3,3,1) +imshow(s1a,[ ]) +title('s1a') +subplot(3,3,4) +imshow(s2a,[ ]) +title('s2a') +subplot(3,3,7) +imshow(s3a,[ ]) +title('s3a') +subplot(3,3,2) +imshow(s1b,[ ]) +title('s1b') +subplot(3,3,5) +imshow(s2b,[ ]) +title('s2b') +subplot(3,3,8) +imshow(s3b,[ ]) +title('s3b') +subplot(3,3,3) +imshow(s1c,[ ]) +title('s1c') +subplot(3,3,6) +imshow(s2c,[ ]) +title('s2c') +subplot(3,3,9) +imshow(s3c,[ ]) +title('s3c') +%} + + +%% superposed (noise-free) Images +PSFsum = sum(sum(PSFo)); +if ( UsePSF == 1 ) + DIoT = conv2(DIo,PSFo,'same')./PSFsum; + S1aT = conv2(s1a,PSFo,'same')./PSFsum; + S2aT = conv2(s2a,PSFo,'same')./PSFsum; + S3aT = conv2(s3a,PSFo,'same')./PSFsum; + S1bT = conv2(s1b,PSFo,'same')./PSFsum; + S2bT = conv2(s2b,PSFo,'same')./PSFsum; + S3bT = conv2(s3b,PSFo,'same')./PSFsum; + S1cT = conv2(s1c,PSFo,'same')./PSFsum; + S2cT = conv2(s2c,PSFo,'same')./PSFsum; + S3cT = conv2(s3c,PSFo,'same')./PSFsum; +else + DIoT = ifft2( fft2(DIo).*fftshift(OTFo) ); + S1aT = ifft2( fft2(s1a).*fftshift(OTFo) ); + S2aT = ifft2( fft2(s2a).*fftshift(OTFo) ); + S3aT = ifft2( fft2(s3a).*fftshift(OTFo) ); + S1bT = ifft2( fft2(s1b).*fftshift(OTFo) ); + S2bT = ifft2( fft2(s2b).*fftshift(OTFo) ); + S3bT = ifft2( fft2(s3b).*fftshift(OTFo) ); + S1cT = ifft2( fft2(s1c).*fftshift(OTFo) ); + S2cT = ifft2( fft2(s2c).*fftshift(OTFo) ); + S3cT = ifft2( fft2(s3c).*fftshift(OTFo) ); + + DIoT = real(DIoT); + S1aT = real(S1aT); + S2aT = real(S2aT); + S3aT = real(S3aT); + S1bT = real(S1bT); + S2bT = real(S2bT); + S3bT = real(S3bT); + S1cT = real(S1cT); + S2cT = real(S2cT); + S3cT = real(S3cT); +end +%{ +figure; +subplot(3,3,1) +imshow(S1aT,[ ]) +title('S1aT') +subplot(3,3,4) +imshow(S2aT,[ ]) +title('S2aT') +subplot(3,3,7) +imshow(S3aT,[ ]) +title('S3aT') +subplot(3,3,2) +imshow(S1bT,[ ]) +title('S1bT') +subplot(3,3,5) +imshow(S2bT,[ ]) +title('S2bT') +subplot(3,3,8) +imshow(S3bT,[ ]) +title('S3bT') +subplot(3,3,3) +imshow(S1cT,[ ]) +title('S1cT') +subplot(3,3,6) +imshow(S2cT,[ ]) +title('S2cT') +subplot(3,3,9) +imshow(S3cT,[ ]) +title('S3cT') +%} + + +%% Gaussian noise generation +aNoise = NoiseLevel/100; % corresponds to 10% noise +% SNR = 1/aNoise +% SNRdb = 20*log10(1/aNoise) +nDIoT = random('norm', 0, aNoise*std2(DIoT), w , w); +nS1aT = random('norm', 0, aNoise*std2(S1aT), w , w); +nS2aT = random('norm', 0, aNoise*std2(S2aT), w , w); +nS3aT = random('norm', 0, aNoise*std2(S3aT), w , w); +nS1bT = random('norm', 0, aNoise*std2(S2bT), w , w); +nS2bT = random('norm', 0, aNoise*std2(S2bT), w , w); +nS3bT = random('norm', 0, aNoise*std2(S2bT), w , w); +nS1cT = random('norm', 0, aNoise*std2(S3cT), w , w); +nS2cT = random('norm', 0, aNoise*std2(S3cT), w , w); +nS3cT = random('norm', 0, aNoise*std2(S3cT), w , w); + +%% noise added raw SIM images +NoiseFrac = 1; %may be set to 0 to avoid noise addition +DIoTnoisy = DIoT + NoiseFrac*nDIoT; +S1aTnoisy = S1aT + NoiseFrac*nS1aT; +S2aTnoisy = S2aT + NoiseFrac*nS2aT; +S3aTnoisy = S3aT + NoiseFrac*nS3aT; +S1bTnoisy = S1bT + NoiseFrac*nS1bT; +S2bTnoisy = S2bT + NoiseFrac*nS2bT; +S3bTnoisy = S3bT + NoiseFrac*nS3bT; +S1cTnoisy = S1cT + NoiseFrac*nS1cT; +S2cTnoisy = S2cT + NoiseFrac*nS2cT; +S3cTnoisy = S3cT + NoiseFrac*nS3cT; +%{ +figure; +subplot(3,3,1) +imshow(S1aTnoisy,[ ]) +title('S1aTnoisy') +subplot(3,3,4) +imshow(S2aTnoisy,[ ]) +title('S2aTnoisy') +subplot(3,3,7) +imshow(S3aTnoisy,[ ]) +title('S3aTnoisy') +subplot(3,3,2) +imshow(S1bTnoisy,[ ]) +title('S1bTnoisy') +subplot(3,3,5) +imshow(S2bTnoisy,[ ]) +title('S2bTnoisy') +subplot(3,3,8) +imshow(S3bTnoisy,[ ]) +title('S3bTnoisy') +subplot(3,3,3) +imshow(S1cTnoisy,[ ]) +title('S1cTnoisy') +subplot(3,3,6) +imshow(S2cTnoisy,[ ]) +title('S2cTnoisy') +subplot(3,3,9) +imshow(S3cTnoisy,[ ]) +title('S3cTnoisy') +%} + +%{ +figure; +imshow(S1aT,[ ]) +title('S1aT') +figure; +imshow(S1aTnoisy,[ ]) +title('S1aTnoisy') + +figure; +hold on +plot(x-wo,S1aT(wo+1,:),'o-','LineWidth',2,'MarkerSize',6) +plot(x-wo,S1aTnoisy(wo+1,:),'r*--','LineWidth',2,'MarkerSize',6) +grid on +box on +%} \ No newline at end of file diff --git a/SIMbasic/SIMo.m b/SIMbasic/SIMo.m new file mode 100644 index 0000000..765b5e6 --- /dev/null +++ b/SIMbasic/SIMo.m @@ -0,0 +1,206 @@ +clear all +close all +clc + +w = 512; +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); + +%% Generation of the PSF with Besselj. +scale = 0.63; % used to adjust PSF/OTF width +[PSFo,OTFo] = PsfOtf(w,scale); +%{ +figure; +mesh(PSFo) +title('system PSF') + +figure; +mesh(OTFo) +title('system OTF') +%} + +%% Reading input file +Io1 = imread('testpat.tiff'); +Io = Io1(257:768,257:768); % selecting central 512x512 of image +DIo = double(Io); +figure; +imshow(DIo,[]) + + +%% Generating raw SIM Images +k2 = 75.23; % illumination freq +ModFac = 0.8; % modulation factor +NoiseLevel = 10; % in percentage +UsePSF = 0; % 1(to blur using PSF), 0(to blur using OTF) +[S1aTnoisy S2aTnoisy S3aTnoisy ... + S1bTnoisy S2bTnoisy S3bTnoisy ... + S1cTnoisy S2cTnoisy S3cTnoisy ... + DIoTnoisy DIoT] = SIMimagesF(k2,DIo,PSFo,OTFo,ModFac,NoiseLevel,UsePSF); +%{ +figure; +imshow(S1aTnoisy,[]) +title('Raw SIM image') +figure; +imshow(S1bTnoisy,[]) +title('Raw SIM image') +figure; +imshow(S1cTnoisy,[]) +title('Raw SIM image') +figure; +imshow(DIoTnoisy,[]) +title('Noisy Wide-Field image') +figure; +imshow(DIoT,[]) +title('Noise-free Wide-Field image') +break +%} + +%% obtaining the noisy estimates of three frequency components +[fAo,fAp,fAm,kA]... + = PCMseparateF(S1aTnoisy,S2aTnoisy,S3aTnoisy,OTFo); +% break +[fBo,fBp,fBm,kB]... + = PCMseparateF(S1bTnoisy,S2bTnoisy,S3bTnoisy,OTFo); +[fCo,fCp,fCm,kC]... + = PCMseparateF(S1cTnoisy,S2cTnoisy,S3cTnoisy,OTFo); + +% averaging the central frequency components +fCent = (fAo + fBo + fCo)/3; + +% Object power parameters determination +OBJparaA = OBJpowerPara(fCent,OTFo); + + +%% Wiener Filtering the noisy frequency components +[fAof,fApf,fAmf,Nao,Nap,Nam,Ma,DoubleMatSize]... + = PCMfilteringF(fAo,fAp,fAm,OTFo,OBJparaA,kA); +[fBof,fBpf,fBmf,Nbo,Nbp,Nbm,Mb,~]... + = PCMfilteringF(fBo,fBp,fBm,OTFo,OBJparaA,kB); +[fCof,fCpf,fCmf,Nco,Ncp,Ncm,Mc,~]... + = PCMfilteringF(fCo,fCp,fCm,OTFo,OBJparaA,kC); + +%% doubling Fourier domain size if necessary +OTFo = OTFdoubling(OTFo,DoubleMatSize); + +%% merging all 9 frequency components using generalized Wiener Filter +[Fsum,Fperi,Fcent] = MergingHeptaletsF(fAof,fApf,fAmf,... + fBof,fBpf,fBmf,fCof,fCpf,fCmf,... + Ma,Mb,Mc,Nao,Nap,Nam,Nbo,Nbp,Nbm,... + Nco,Ncp,Ncm,kA,kB,kC,OBJparaA,OTFo); + +% Plotting SIM results +SIMplot(Fsum,Fperi,Fcent,OTFo,kA,kB,kC,S1aTnoisy); +break + +%% recontructed SIM images +Dcent = real( ifft2(fftshift(Fcent)) ); +Dsum = real( ifft2(fftshift(Fsum)) ); +Dperi = real( ifft2(fftshift(Fperi)) ); + +%{ +figure; +mesh(log(abs(Fsum))) +figure; +mesh(log(abs(Fperi))) +%} + +w = size(OTFo,1); +h = 30; % pixel width to be trimed of the image edge to trim of artifacts +figure; +imshow(Dcent(h+1:t-h,h+1:t-h),[]) +title('Wiener Filtered wide-field') +figure; +imshow(Dsum(h+1:t-h,h+1:t-h),[]) +title('SIM image') +figure; +imshow(Dperi(h+1:t-h,h+1:t-h),[]) +title('SIM image (using only off-center frequency components)') + +%% appodizing the merged frequency components +Index = 0.4; +Kotf = OTFedgeF(OTFo); +[FsumA] = ApodizationFunction(Fsum,kA,kB,kC,Kotf,Index); +[FperiA] = ApodizationFunction(Fperi,kA,kB,kC,Kotf,Index); +DsumA = real( ifft2(fftshift(FsumA)) ); +DperiA = real( ifft2(fftshift(FperiA)) ); + +figure; +imshow(DsumA(h+1:t-h,h+1:t-h),[]) +title('appodized SIM image') +figure; +imshow(DperiA(h+1:t-h,h+1:t-h),[]) +title('appodized SIM image (using only off-center frequency components)') +break +%% for writing the image files into *.tiff files +%{ +h = 1*30; +imwrite(im2uint16(mat2gray(Dcent(h+1:t-h,h+1:t-h))),['Dcent.tif'],'tiff'); +imwrite(im2uint16(mat2gray(Dsum(h+1:t-h,h+1:t-h))),['Dsum.tif'],'tiff'); +imwrite(im2uint16(mat2gray(Dperi(h+1:t-h,h+1:t-h))),['Dperi.tif'],'tiff'); +imwrite(im2uint16(mat2gray(DsumA(h+1:t-h,h+1:t-h))),['DsumA.tif'],'tiff'); +imwrite(im2uint16(mat2gray(DperiA(h+1:t-h,h+1:t-h))),['DperiA.tif'],'tiff'); +%} + +%% ploting FT of images +fDIo = fftshift(fft2(DIo)); +fDIoT = fftshift(fft2(DIoT)); +fDIoTnoisy = fftshift(fft2(DIoTnoisy)); +fS1aTnoisy = fftshift(fft2(S1aTnoisy)); + +p = 10; +minL1 = min(min( abs(fDIo).^(1/p) )); +minL2 = min(min( abs(fDIoT).^(1/p) )); +minL3 = min(min( abs(fDIoTnoisy).^(1/p) )); +minL4 = min(min( abs(fS1aTnoisy).^(1/p) )); +minL5 = min(min( abs(Fcent).^(1/p) )); +minL6 = min(min( abs(Fsum).^(1/p) )); +minL7 = min(min( abs(Fperi).^(1/p) )); +maxL1 = max(max( abs(fDIo).^(1/p) )); +maxL2 = max(max( abs(fDIoT).^(1/p) )); +maxL3 = max(max( abs(fDIoTnoisy).^(1/p) )); +maxL4 = max(max( abs(fS1aTnoisy).^(1/p) )); +maxL5 = max(max( abs(Fcent).^(1/p) )); +maxL6 = max(max( abs(Fsum).^(1/p) )); +maxL7 = max(max( abs(Fperi).^(1/p) )); +minL = min([minL1,minL2,minL3,minL4,minL5,minL6,minL7]); +maxL = max([maxL1,maxL2,maxL3,maxL4,maxL5,maxL6,maxL7]); + +figure; +imshow(abs(fDIo).^(1/p),[minL maxL]) +title('fDIo') +figure; +imshow(abs(fDIoT).^(1/p),[minL maxL]) +title('fDIoT') +figure; +imshow(abs(fDIoTnoisy).^(1/p),[minL maxL]) +title('fDIoTnoisy') +figure; +imshow(abs(fS1aTnoisy).^(1/p),[minL maxL]) +title('fS1aTnoisy') + +figure; +imshow(abs(Fcent).^(1/p),[minL maxL]) +title('Fcent') +figure; +imshow(abs(Fsum).^(1/p),[minL maxL]) +title('Fsum') +figure; +imshow(abs(Fperi).^(1/p),[minL maxL]) +title('Fperi') +figure; +imshow(abs(FsumA).^(1/p),[minL maxL]) +title('FsumA') +figure; +imshow(abs(FperiA).^(1/p),[minL maxL]) +title('FperiA') + +%% for writing the image files into *.tiff files +%{ +imwrite(im2uint16(mat2gray(abs(Fcent).^(1/p))),['Fcent.tif'],'tiff'); +imwrite(im2uint16(mat2gray(abs(Fsum).^(1/p))),['Fsum.tif'],'tiff'); +imwrite(im2uint16(mat2gray(abs(Fperi).^(1/p))),['Fperi.tif'],'tiff'); +imwrite(im2uint16(mat2gray(abs(FsumA).^(1/p))),['FsumA.tif'],'tiff'); +imwrite(im2uint16(mat2gray(abs(FperiA).^(1/p))),['FperiA.tif'],'tiff'); +%} diff --git a/SIMbasic/SIMplot.m b/SIMbasic/SIMplot.m new file mode 100644 index 0000000..b83fd74 --- /dev/null +++ b/SIMbasic/SIMplot.m @@ -0,0 +1,84 @@ +function [] = SIMplot(Fsum,Fperi,Fcent,OTFo,kA,kB,kC,S1aTnoisy) + +%% recontructed SIM images +Dcent = real( ifft2(fftshift(Fcent)) ); +Dsum = real( ifft2(fftshift(Fsum)) ); +Dperi = real( ifft2(fftshift(Fperi)) ); + +t = size(OTFo,1); +h = 1*30; % for removing the image edges +figure; +imshow(Dcent(h+1:t-h,h+1:t-h),[]) +title('Wiener-Filtered wide-field') +figure; +imshow(Dsum(h+1:t-h,h+1:t-h),[]) +title('SIM image') +figure; +imshow(Dperi(h+1:t-h,h+1:t-h),[]) +title('SIM image (using only off-center frequency components)') + +% appodizing the merged frequency components +Index = 0.4; +Kotf = OTFedgeF(OTFo); +[FsumA] = ApodizationFunction(Fsum,kA,kB,kC,Kotf,Index); +[FperiA] = ApodizationFunction(Fperi,kA,kB,kC,Kotf,Index); +DsumA = real( ifft2(fftshift(FsumA)) ); +DperiA = real( ifft2(fftshift(FperiA)) ); + +figure; +imshow(DsumA(h+1:t-h,h+1:t-h),[]) +title('appodized SIM image') +figure; +imshow(DperiA(h+1:t-h,h+1:t-h),[]) +title('appodized SIM image (using only off-center frequency components)') + + +%% Frequency Plots +fS1aTnoisy = fftshift(fft2(S1aTnoisy)); +w = size(OTFo,1); +wo = w/2; +w1 = size(fS1aTnoisy,1); +if ( w > w1 ) + fS1aTnoisy0 = zeros(w,w); + fS1aTnoisy0(wo-w1/2+1:wo+w1/2,wo-w1/2+1:wo+w1/2) = fS1aTnoisy; + clear fS1aTnoisy + fS1aTnoisy = fS1aTnoisy0; + clear fS1aTnoisy0; +end + + +p = 10; +minL1 = min(min( abs(fS1aTnoisy).^(1/p) )); +minL2 = min(min( abs(Fcent).^(1/p) )); +minL3 = min(min( abs(Fsum).^(1/p) )); +minL4 = min(min( abs(Fperi).^(1/p) )); +minL5 = min(min( abs(FsumA).^(1/p) )); +maxL1 = max(max( abs(fS1aTnoisy).^(1/p) )); +maxL2 = max(max( abs(Fcent).^(1/p) )); +maxL3 = max(max( abs(Fsum).^(1/p) )); +maxL4 = max(max( abs(Fperi).^(1/p) )); +maxL5 = max(max( abs(FsumA).^(1/p) )); +minL = min([minL1,minL2,minL3,minL4,minL5]); +maxL = max([maxL1,maxL2,maxL3,maxL4,maxL5]); + +figure; +imshow(abs(fS1aTnoisy).^(1/p),[minL maxL]) +title('fS1aTnoisy') + +figure; +imshow(abs(Fcent).^(1/p),[minL maxL]) +title('Weiner Filtered frequency') +figure; +imshow(abs(Fsum).^(1/p),[minL maxL]) +title('SIM frequency') +figure; +imshow(abs(Fperi).^(1/p),[minL maxL]) +title('SIM (off-center frequency components)') +figure; +imshow(abs(FsumA).^(1/p),[minL maxL]) +title('appodized SIM frequency') +figure; +imshow(abs(FperiA).^(1/p),[minL maxL]) +title('appodized SIM (off-center frequency components)') + + diff --git a/SIMbasic/SeparatedComponents2D.m b/SIMbasic/SeparatedComponents2D.m new file mode 100644 index 0000000..14d3880 --- /dev/null +++ b/SIMbasic/SeparatedComponents2D.m @@ -0,0 +1,22 @@ +function [FiSMao,FiSMap,FiSMam] = SeparatedComponents2D(... + phaseShift,phaseShift0,FcS1aT,FcS2aT,FcS3aT) +% Aim: Unmixing the frequency components of raw SIM images +% phaseShift,phaseShift0: illumination phase shifts +% FcS1aT,FcS2aT,FcS3aT: FT of raw SIM images +% FiSMao,FiSMap,FiSMam: unmixed frequency components of raw SIM images + +phaseShift1 = phaseShift(1,1); +phaseShift2 = phaseShift(2,1); +MF = 1.0; +%% Transformation Matrix +M = 0.5*[1 0.5*MF*exp(-1i*phaseShift0) 0.5*MF*exp(+1i*phaseShift0); + 1 0.5*MF*exp(-1i*phaseShift1) 0.5*MF*exp(+1i*phaseShift1); + 1 0.5*MF*exp(-1i*phaseShift2) 0.5*MF*exp(+1i*phaseShift2)]; + +%% Separting the components +%=========================================================== +Minv = inv(M); + +FiSMao = Minv(1,1)*FcS1aT + Minv(1,2)*FcS2aT + Minv(1,3)*FcS3aT; +FiSMap = Minv(2,1)*FcS1aT + Minv(2,2)*FcS2aT + Minv(2,3)*FcS3aT; +FiSMam = Minv(3,1)*FcS1aT + Minv(3,2)*FcS2aT + Minv(3,3)*FcS3aT; diff --git a/SIMbasic/TripletSNR0.m b/SIMbasic/TripletSNR0.m new file mode 100644 index 0000000..6bf5b1d --- /dev/null +++ b/SIMbasic/TripletSNR0.m @@ -0,0 +1,66 @@ +function [SIGao,SIGap2,SIGam2] = TripletSNR0(OBJpara,k2fa,OTFo,fDIp) + +% AIM: To obtain signal spectrums corresponding to central and off-center +% frequency components +% INPUT VARIABLES +% OBJpara: object power parameters +% k2fa: illumination frequency vector +% OTFo: system OTF +% fDIp: one of the off-center frequency component (utilized here only for +% visual verification of computation) +% OUTPUT VARIABLES +% SIGao: signal spectrum corresponding to central frequency component +% SIGap2,SIGam2: signal spectrums corresponding to off-center frequency components + + +w = size(OTFo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Cv = (X-wo) + 1i*(Y-wo); +Ro = abs(Cv); + +% object spectrum parameters +Aobj = OBJpara(1); +Bobj = OBJpara(2); + +% object spectrums (default) +kv = k2fa(2) + 1i*k2fa(1); % vector along illumination direction +Rp = abs(Cv-kv); +Rm = abs(Cv+kv); +OBJo = Aobj*(Ro.^Bobj); +OBJp = Aobj*(Rp.^Bobj); +OBJm = Aobj*(Rm.^Bobj); + +OBJo(wo+1,wo+1) = 0.25*OBJo(wo+2,wo+1) + 0.25*OBJo(wo+1,wo+2)... + + 0.25*OBJo(wo+0,wo+1) + 0.25*OBJo(wo+1,wo+0); + +k3 = round(k2fa); +OBJp(wo+1+k3(1),wo+1+k3(2)) = 0.25*OBJp(wo+2+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+2+k3(2))... + + 0.25*OBJp(wo+0+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+0+k3(2)); +OBJm(wo+1-k3(1),wo+1-k3(2)) = 0.25*OBJm(wo+2-k3(1),wo+1-k3(2))... + + 0.25*OBJm(wo+1-k3(1),wo+2-k3(2))... + + 0.25*OBJm(wo+0-k3(1),wo+1-k3(2))... + + 0.25*OBJm(wo+1-k3(1),wo+0-k3(2)); + +% signal spectrums +SIGao = OBJo.*OTFo; +SIGap = OBJp.*OTFo; +SIGam = OBJm.*OTFo; + +SIGap2 = circshift(SIGap,-k3); +SIGam2 = circshift(SIGam,k3); + +%% for visual verification +%{ +pp = 3; +figure; +hold on +plot([0:w-1]-wo,log(abs(SIGap2(wo+pp,:))),'k--','LineWidth',3,'MarkerSize',6) +plot([0:w-1]-wo,log(abs(fDIp(wo+pp,:))),'mo-','LineWidth',2,'MarkerSize',6) +grid on +box on +%} \ No newline at end of file diff --git a/SIMbasic/WoFilterCenter.m b/SIMbasic/WoFilterCenter.m new file mode 100644 index 0000000..8299473 --- /dev/null +++ b/SIMbasic/WoFilterCenter.m @@ -0,0 +1,57 @@ +function [FiSMaof,NoisePower] = WoFilterCenter(FiSMao,OTFo,co,OBJpara,SFo) +% Aim: Wiener Filtering the central frequency component +% INPUT VARIABLES +% FiSMao: noisy central frequency component +% OTFo: system OTF +% co: Wiener filter constant [=1, for minimum RMS estimate] +% SFo: scaling factor (not significant here, so set to 1) +% OUTPUT VARIABLES +% FiSMaof: Wiener Filtered estimate of FiSMao +% NoisePower: avg. noise power in FiSMao + +w = size(FiSMao,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Ro = sqrt( (X-wo).^2 + (Y-wo).^2 ); + +OTFpower = OTFo.*conj(OTFo); + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +% frequency beyond which NoisePower estimate to be computed +NoiseFreq = Kotf + 20; + +% NoisePower determination +Zo = Ro>NoiseFreq; +nNoise = FiSMao.*Zo; +NoisePower = sum(sum( nNoise.*conj(nNoise) ))./sum(sum(Zo)); + +% Object Power determination +Aobj = OBJpara(1); +Bobj = OBJpara(2); +Ro(wo+1,wo+1) = 1; +OBJpower = Aobj*(Ro.^Bobj); +OBJpower = OBJpower.^2; + +%% Wiener Filtering +FiSMaof = FiSMao.*(SFo.*conj(OTFo)./NoisePower)./((SFo.^2).*OTFpower./NoisePower + co./OBJpower); + +%% for cross-checking filtered estimate visually +%{ +WFilter = (SFo.^2.*OTFpower./NoisePower)./((SFo.^2).*OTFpower./NoisePower + co./OBJpower); +FiSMao1 = FiSMaof.*OTFo; +pp = 3; +figure; +hold on +plot(x-wo,log(abs(FiSMaof(wo+pp,:))),'go--','LineWidth',2,'MarkerSize',6) +plot(x-wo,log(abs(FiSMao(wo+pp,:))),'o--','LineWidth',2,'MarkerSize',6) +plot(x-wo,log(abs(FiSMao1(wo+pp,:))),'r*--','LineWidth',2,'MarkerSize',4) +plot(x-wo,10*WFilter(wo+pp,:),'k*--','LineWidth',2,'MarkerSize',4) +title('WoFilter') +legend('FiSMaof','FiSMao','FiSMao1') +grid on +box on +%} \ No newline at end of file diff --git a/SIMbasic/WoFilterSideLobe.m b/SIMbasic/WoFilterSideLobe.m new file mode 100644 index 0000000..fb717c5 --- /dev/null +++ b/SIMbasic/WoFilterSideLobe.m @@ -0,0 +1,54 @@ +function [FiSMaof,NoisePower] = WoFilterSideLobe(FiSMao,OTFo,co,OBJsideP,SFo) +% Aim: Wiener Filtering the off-center frequency component +% INPUT VARIABLES +% FiSMao: noisy off-center frequency component +% OTFo: system OTF +% co: Wiener filter constant [=1, for minimum RMS estimate] +% OBJsideP: avg. object spectrum +% SFo: modulation factor +% OUTPUT VARIABLES +% FiSMaof: Wiener Filtered estimate of FiSMao +% NoisePower: avg. noise power in FiSMao + +w = size(FiSMao,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Ro = sqrt( (X-wo).^2 + (Y-wo).^2 ); + +OTFpower = OTFo.*conj(OTFo); + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +% frequency beyond which NoisePower estimate to be computed +NoiseFreq = Kotf + 20; + +% NoisePower determination +Zo = Ro>NoiseFreq; +nNoise = FiSMao.*Zo; +NoisePower = sum(sum( nNoise.*conj(nNoise) ))./sum(sum(Zo)); + +% Object Power determination +OBJpower = OBJsideP.^2; + +%% Wiener Filtering +FiSMaof = FiSMao.*(SFo.*conj(OTFo)./NoisePower)./((SFo.^2).*OTFpower./NoisePower + co./OBJpower); + +%% for cross-checking filtered estimate visually +%{ +WFilter = (SFo.^2.*OTFpower./NoisePower)./((SFo.^2).*OTFpower./NoisePower + co./OBJpower); +FiSMao1 = FiSMaof.*OTFo; +pp = 3; +figure; +hold on +plot(x-wo,log(abs(FiSMaof(wo+pp,:))),'go--','LineWidth',2,'MarkerSize',6) +plot(x-wo,log(abs(FiSMao(wo+pp,:))),'o--','LineWidth',2,'MarkerSize',6) +plot(x-wo,log(abs(FiSMao1(wo+pp,:))),'r*--','LineWidth',2,'MarkerSize',4) +plot(x-wo,10*WFilter(wo+pp,:),'k*--','LineWidth',2,'MarkerSize',4) +title('WoFilter') +legend('FiSMaof','FiSMao','FiSMao1') +grid on 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vPCDlN4Yl(wZ!IR@SU)dowuHJ)-mHf>*J>t@%`+0S?~V=PLxy= literal 0 HcmV?d00001 diff --git a/SIMexpt/ApodizationFunction.m b/SIMexpt/ApodizationFunction.m new file mode 100644 index 0000000..172f322 --- /dev/null +++ b/SIMexpt/ApodizationFunction.m @@ -0,0 +1,30 @@ +function [FsumA] = ApodizationFunction(Fsum,k2fa,k2fb,k2fc,Kotf,Index) + +t = size(Fsum,1); + +OTFo_mask = OTFmaskShifted(0.*k2fa,Kotf,t); +OTFap_mask = OTFmaskShifted(k2fa,Kotf,t); +OTFam_mask = OTFmaskShifted(-k2fa,Kotf,t); +OTFbp_mask = OTFmaskShifted(k2fb,Kotf,t); +OTFbm_mask = OTFmaskShifted(-k2fb,Kotf,t); +OTFcp_mask = OTFmaskShifted(k2fc,Kotf,t); +OTFcm_mask = OTFmaskShifted(-k2fc,Kotf,t); +ApoMask = OTFo_mask.*OTFap_mask.*OTFam_mask.*OTFbp_mask.*OTFbm_mask.*OTFcp_mask.*OTFcm_mask; +clear OTFoz OTFo_mask OTFap_mask OTFam_mask OTFbp_mask OTFbm_mask OTFcp_mask OTFcm_mask +%{ +figure; +imshow(ApoMask,[ ]) +%} + +DistApoMask = bwdist(ApoMask); +maxApoMask = max(max(DistApoMask)); +ApoFunc = double(DistApoMask./maxApoMask).^Index; +%{ +figure; +imshow(DistApoMask,[ ]) +figure; +mesh(double(ApoFunc)) +%} + +FsumA = Fsum.*ApoFunc; +clear ApoMask DistApoMask ApoFunc \ No newline at end of file diff --git a/SIMexpt/ApproxFreqDuplex.m b/SIMexpt/ApproxFreqDuplex.m new file mode 100644 index 0000000..a912bd5 --- /dev/null +++ b/SIMexpt/ApproxFreqDuplex.m @@ -0,0 +1,28 @@ +function [maxK2,Ix,Iy] = ApproxFreqDuplex(FiSMap,Kotf) +% AIM: approx. illumination frequency vector determination +% INPUT VARIABLES +% FiSMap: FT of raw SIM image +% Kotf: OTF cut-off frequency +% OUTPUT VARIABLES +% maxK2: illumination frequency vector (approx) +% Ix,Iy: coordinates of illumination frequency peaks + +FiSMap = abs(FiSMap); + +w = size(FiSMap,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); + +Ro = sqrt( (X-wo).^2 + (Y-wo).^2 ); +Z0 = Ro > round(0.5*Kotf); +Z1 = X > wo; + +FiSMap = FiSMap.*Z0.*Z1; +dumY = max( FiSMap,[],1 ); +[dummy Iy] = max(dumY); +dumX = max( FiSMap,[],2 ); +[dummy Ix] = max(dumX); + +maxK2 = [Ix-(wo+1) Iy-(wo+1)]; diff --git a/SIMexpt/BgNormalization0.m b/SIMexpt/BgNormalization0.m new file mode 100644 index 0000000..7d550b1 --- /dev/null +++ b/SIMexpt/BgNormalization0.m @@ -0,0 +1,39 @@ +function [S1aTnoisyA, S2aTnoisyA, S3aTnoisyA, ... + S1bTnoisyA, S2bTnoisyA, S3bTnoisyA, ... + S1cTnoisyA, S2cTnoisyA, S3cTnoisyA] = BgNormalization0(... + S1aTnoisy, S2aTnoisy, S3aTnoisy, ... + S1bTnoisy, S2bTnoisy, S3bTnoisy, ... + S1cTnoisy, S2cTnoisy, S3cTnoisy) + +m1a = mean2(S1aTnoisy); +m2a = mean2(S2aTnoisy); +m3a = mean2(S3aTnoisy); +m1b = mean2(S1bTnoisy); +m2b = mean2(S2bTnoisy); +m3b = mean2(S3bTnoisy); +m1c = mean2(S1cTnoisy); +m2c = mean2(S2cTnoisy); +m3c = mean2(S3cTnoisy); + +s1a = std(S1aTnoisy(:)); +s2a = std(S2aTnoisy(:)); +s3a = std(S3aTnoisy(:)); +s1b = std(S1bTnoisy(:)); +s2b = std(S2bTnoisy(:)); +s3b = std(S3bTnoisy(:)); +s1c = std(S1cTnoisy(:)); +s2c = std(S2cTnoisy(:)); +s3c = std(S3cTnoisy(:)); + +mTemp = max([m1a m2a m3a m1b m2b m3b m1c m2c m3c]); +sTemp = max([s1a s2a s3a s1b s2b s3b s1c s2c s3c]); + +S1aTnoisyA = (S1aTnoisy - m1a).*(sTemp./s1a) + mTemp; +S2aTnoisyA = (S2aTnoisy - m2a).*(sTemp./s2a) + mTemp; +S3aTnoisyA = (S3aTnoisy - m3a).*(sTemp./s3a) + mTemp; +S1bTnoisyA = (S1bTnoisy - m1b).*(sTemp./s1b) + mTemp; +S2bTnoisyA = (S2bTnoisy - m2b).*(sTemp./s2b) + mTemp; +S3bTnoisyA = (S3bTnoisy - m3b).*(sTemp./s3b) + mTemp; +S1cTnoisyA = (S1cTnoisy - m1c).*(sTemp./s1c) + mTemp; +S2cTnoisyA = (S2cTnoisy - m2c).*(sTemp./s2c) + mTemp; +S3cTnoisyA = (S3cTnoisy - m3c).*(sTemp./s3c) + mTemp; \ No newline at end of file diff --git a/SIMexpt/IlluminationFreqF.m b/SIMexpt/IlluminationFreqF.m new file mode 100644 index 0000000..5b87d16 --- /dev/null +++ b/SIMexpt/IlluminationFreqF.m @@ -0,0 +1,38 @@ +function [k2fa] = IlluminationFreqF(S1aTnoisy,OTFo) +% AIM: illumination frequency vector determination +% INPUT VARIABLES +% S1aTnoisy: raw SIM image +% OTFo: system OTF +% OUTPUT VARIABLE +% k2fa: illumination frequency vector + +w = size(OTFo,1); +wo = w/2; + +% computing PSFe for edge tapering SIM images (heuristically determined) +PSFd = real(fftshift( ifft2(fftshift(OTFo.^10)) )); +PSFd = PSFd/max(max(PSFd)); +PSFd = PSFd/sum(sum(PSFd)); +h = 30; +PSFe = PSFd(wo-h+1:wo+h,wo-h+1:wo+h); + +% edge tapering raw SIM image +S1aTnoisy_et = edgetaper(S1aTnoisy,PSFe); +fS1aTnoisy_et = fftshift(fft2(S1aTnoisy_et)); + +% OTF cut-off freq +Kotf = OTFedgeF(OTFo); + +% Approx illumination frequency vector +[k2fa,~,~] = ApproxFreqDuplex(fS1aTnoisy_et,Kotf); + +fS1aTnoisy = fftshift(fft2(S1aTnoisy)); +% illumination frequency vector determination by optimizing +% autocorrelation of fS1aTnoisy +OPT = 1; +PhaseKai2opt0 = @(k2fa0)PhaseKai2opt(k2fa0,fS1aTnoisy,OTFo,OPT); +options = optimset('LargeScale','off','Algorithm',... + 'active-set','MaxFunEvals',500,'MaxIter',500,'Display','notify'); +k2fa0 = k2fa; +[k2fa,fval] = fminsearch(PhaseKai2opt0,k2fa0,options); +% k2a = sqrt(k2fa*k2fa') diff --git a/SIMexpt/IlluminationPhaseF.m b/SIMexpt/IlluminationPhaseF.m new file mode 100644 index 0000000..2898568 --- /dev/null +++ b/SIMexpt/IlluminationPhaseF.m @@ -0,0 +1,14 @@ +function [phaseA1] = IlluminationPhaseF(S1aTnoisy,k2fa) +% AIM: illumination phase shift determination +% INPUT VARIABLES +% S1aTnoisy: raw SIM image +% k2fa: illumination frequency vector +% OUTPUT VARIABLE +% phaseA1: illumination phase shift determined + +PatternPhaseOpt0 = @(phaseA0)PatternPhaseOpt(phaseA0,S1aTnoisy,k2fa); +options = optimset('LargeScale','off','Algorithm',... + 'active-set','MaxFunEvals',500,'MaxIter',500,'Display','notify'); +phaseA0 = 0; +[phaseA1,fval] = fminsearch(PatternPhaseOpt0,phaseA0,options); +% phaseA1*180/pi \ No newline at end of file diff --git a/SIMexpt/MergingHeptaletsF.m b/SIMexpt/MergingHeptaletsF.m new file mode 100644 index 0000000..d1b915b --- /dev/null +++ b/SIMexpt/MergingHeptaletsF.m @@ -0,0 +1,65 @@ +function [Fsum,Fperi,Fcent] = MergingHeptaletsF(fDIo,fDIp,fDIm,fDBo,fDBp,fDBm,... + fDCo,fDCp,fDCm,Ma,Mb,Mc,npDIo,npDIp,npDIm,... + npDBo,npDBp,npDBm,npDCo,npDCp,npDCm,k2fa,k2fb,k2fc,OBJpara,OTFo) + +% AIM: To merge all 9 frequency components into one using generalized +% Wiener Filter +% INPUT VARIABLES +% [fDIo fDIp fDIm +% fDBo fDBp fDBm +% fDCo fDCp fDCm]: nine frequency components +% Ma,Mb,Mc: modulation factors for the three illumination orientations +% [npDIo npDIp npDIm +% npDBo npDBp npDBm +% npDCo,npDCp,npDCm]: noise powers corresponding to nine frequency +% components +% k2fa,k2fb,k2fc: illumination frequency vectors for the three +% illumination orientations +% OBJpara: Object spectrum parameters +% OTFo: system OTF +% OUTPUT VARIABLES +% Fsum: all nine frequency components merged into one using +% generalised Wiener Filter +% Fperi: six off-center frequency components merged into one using +% generalised Wiener Filter +% Fcent: averaged of the three central frequency components + +% obtain signal spectrums corresponding to central and off-center +% frequency components +[SIGao,SIGam2,SIGap2] = TripletSNR0(OBJpara,k2fa,OTFo,fDIm); +[SIGbo,SIGbm2,SIGbp2] = TripletSNR0(OBJpara,k2fb,OTFo,fDBm); +[SIGco,SIGcm2,SIGcp2] = TripletSNR0(OBJpara,k2fc,OTFo,fDCm); + +SIGap2 = Ma*SIGap2; +SIGam2 = Ma*SIGam2; +SIGbp2 = Mb*SIGbp2; +SIGbm2 = Mb*SIGbm2; +SIGcp2 = Mc*SIGcp2; +SIGcm2 = Mc*SIGcm2; + +%% Generalized Wiener-Filter computation +SNRao = SIGao.*conj(SIGao)./npDIo; +SNRap = SIGap2.*conj(SIGap2)./npDIp; +SNRam = SIGam2.*conj(SIGam2)./npDIm; + +SNRbo = SIGbo.*conj(SIGbo)./npDBo; +SNRbp = SIGbp2.*conj(SIGbp2)./npDBp; +SNRbm = SIGbm2.*conj(SIGbm2)./npDBm; + +SNRco = SIGco.*conj(SIGco)./npDCo; +SNRcp = SIGcp2.*conj(SIGcp2)./npDCp; +SNRcm = SIGcm2.*conj(SIGcm2)./npDCm; + +ComDeno = 0.01 + ( SNRao + SNRap + SNRam + SNRbo + SNRbp + SNRbm + SNRco + SNRcp + SNRcm ); +Fsum = fDIo.*SNRao + fDIp.*SNRap + fDIm.*SNRam... + + fDBo.*SNRbo + fDBp.*SNRbp + fDBm.*SNRbm... + + fDCo.*SNRco + fDCp.*SNRcp + fDCm.*SNRcm; +Fsum = Fsum./ComDeno; + +ComPeri = 0.01 + ( SNRap + SNRam + SNRbp + SNRbm + SNRcp + SNRcm ); +Fperi = fDIp.*SNRap + fDIm.*SNRam + fDBp.*SNRbp + fDBm.*SNRbm... + + fDCp.*SNRcp + fDCm.*SNRcm; +Fperi = Fperi./ComPeri; + +% averaged central frequency component +Fcent = (fDIo+fDBo+fDCo)/3; diff --git a/SIMexpt/ModulationFactor.m b/SIMexpt/ModulationFactor.m new file mode 100644 index 0000000..4ce0313 --- /dev/null +++ b/SIMexpt/ModulationFactor.m @@ -0,0 +1,86 @@ +function Mm = ModulationFactor(fDp,k1a,OBJparaA,OTFo) +% AIM: Determination of modulation factor +% INPUT VARIABLES +% fDp: off-center frequency component +% k1a: illumination frequency vector +% OBJparaA: Object power parameters +% OTFo: system OTF +% OUTPUT VARIABLE +% Mm: modulation factor + +w = size(OTFo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Cv = (X-wo) + 1i*(Y-wo); +Ro = abs(Cv); + +% magnitude of illumination vector +k2 = sqrt(k1a*k1a'); + +% vector along illumination direction +kv = k1a(2) + 1i*k1a(1); +Rp = abs(Cv+kv); + +% Object power parameters +Aobj = OBJparaA(1); +Bobj = OBJparaA(2); + +% Object spectrum +OBJp = Aobj*(Rp+0).^Bobj; + +% illumination vector rounded to nearest pixel +k3 = -round(k1a); + +OBJp(wo+1+k3(1),wo+1+k3(2)) = 0.25*OBJp(wo+2+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+2+k3(2))... + + 0.25*OBJp(wo+0+k3(1),wo+1+k3(2))... + + 0.25*OBJp(wo+1+k3(1),wo+0+k3(2)); + +% signal spectrum +SIGap = OBJp.*OTFo; + +% figure; +% mesh(log(abs(OBJp))) +% figure; +% mesh(log(abs(fDp))) + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +% frequency beyond which NoisePower estimate to be computed +NoiseFreq = Kotf + 20; + +% NoisePower determination +Zo = Ro>NoiseFreq; +nNoise = fDp.*Zo; +NoisePower = sum(sum( nNoise.*conj(nNoise) ))./sum(sum(Zo)); + +% Noise free object power computation +Fpower = fDp.*conj(fDp) - NoisePower; +fDp = sqrt(abs(Fpower)); + +% frequency range over which signal power matching is done to estimate +% modulation factor +Zmask = (Ro > 0.2*k2).*(Ro < 0.8*k2).*(Rp > 0.2*k2); + +% least square approximation for modulation factor +Mm = sum(sum(SIGap.*abs(fDp).*Zmask)); +Mm = Mm./sum(sum(SIGap.^2.*Zmask)); + +%% for visual verification +%{ +pp = 3; +figure; +hold on +plot(x-wo,log(abs(fDp(wo+pp,:))),'o-','LineWidth',2,'MarkerSize',6) +plot(x-wo,log(abs(SIGap(wo+pp,:))),'go--','LineWidth',2,'MarkerSize',4) +plot(x-wo,log(abs(Mm*SIGap(wo+pp,:))),'r*--','LineWidth',2,'MarkerSize',4) +grid on +box on +kk +%} + + + diff --git a/SIMexpt/OBJparaOpt.m b/SIMexpt/OBJparaOpt.m new file mode 100644 index 0000000..8c17130 --- /dev/null +++ b/SIMexpt/OBJparaOpt.m @@ -0,0 +1,48 @@ +function Esum = OBJparaOpt(OBJpara0,fDIoTnoisy,OTFo) +% AIM: Determined Sum of Squared Errors (SSE) between `actual signal power' and +% `approximated signal power' +% INPUT VARIABLES +% OBJpara0: [Aobj Bobj], Object power parameters +% fDIoTnoisy: FT of central frequency component +% OTFo: system OTF +% OUTPUT VARIABLE +% Esum: SSE between `actual signal spectrum' and `approximated signal +% spectrum' + +w = size(OTFo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Cv = (X-wo) + 1i*(Y-wo); +Ro = abs(Cv); +Ro(wo+1,wo+1) = 1; % to avoid nan + +% approximated signal power calculation +Aobj = OBJpara0(1); +Bobj = OBJpara0(2); +OBJpower = Aobj*(Ro.^Bobj); +SIGpower = OBJpower.*OTFo; + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +% range of frequency over which SSE is computed +Zloop = (Ro<0.75*Kotf).*(Ro>0.25*Kotf); + +% frequency beyond which NoisePower estimate to be computed +NoiseFreq = Kotf + 20; + +% NoisePower determination +Zo = Ro>NoiseFreq; +nNoise = fDIoTnoisy.*Zo; +NoisePower = sum(sum( nNoise.*conj(nNoise) ))./sum(sum(Zo)); + +% Noise free object power computation +Fpower = fDIoTnoisy.*conj(fDIoTnoisy) - NoisePower; +fDIoTnoisy = sqrt(abs(Fpower)); + +% SSE computation +Error = fDIoTnoisy - SIGpower; +Esum = sum(sum((Error.^2./Ro).*Zloop)); + diff --git a/SIMexpt/OBJpowerPara.m b/SIMexpt/OBJpowerPara.m new file mode 100644 index 0000000..9ef86ce --- /dev/null +++ b/SIMexpt/OBJpowerPara.m @@ -0,0 +1,48 @@ +function OBJparaA = OBJpowerPara(fDIoTnoisy,OTFo) +% AIM: determination of object power parameters Aobj and Bobj +% INPUT VARIABLES +% fDIoTnoisy: FT of central frequency component +% OTFo: system OTFo +% OUTPUT VARIABLES +% OBJparaA: [Aobj Bobj] + +w = size(OTFo,1); +wo = w/2; +x = linspace(0,w-1,w); +y = linspace(0,w-1,w); +[X,Y] = meshgrid(x,y); +Cv = (X-wo) + 1i*(Y-wo); +Ro = abs(Cv); + +% OTF cut-off frequency +Kotf = OTFedgeF(OTFo); + +%% object power parameters through optimization +OBJparaOpt0 = @(OBJpara0)OBJparaOpt(OBJpara0,fDIoTnoisy,OTFo); +options = optimset('LargeScale','off','Algorithm',... + 'active-set','MaxFunEvals',500,'MaxIter',500,'Display','notify'); + +% obtaining crude initial guesses for Aobj and Bobj +Zm = (Ro>0.3*Kotf).*(Ro<0.4*Kotf); +Aobj = sum(sum(abs(fDIoTnoisy.*Zm)))./sum(sum(Zm)); +Bobj = -0.5; +OBJpara0 = [Aobj Bobj]; + +% optimization step +[OBJparaA,fval] = fminsearch(OBJparaOpt0,OBJpara0,options); + +%% plot for cross-checking the result +%{ +Aobj = OBJparaA(1); +Bobj = OBJparaA(2); +OBJo = Aobj*(Ro.^Bobj); +SIGp = OBJo.*OTFo; +pp = 3; +figure; +hold on +plot([0:w-1]-wo,log(abs(fDIoTnoisy(wo+pp,:))),'k--','LineWidth',3,'MarkerSize',6) +plot([0:w-1]-wo,log(abs(SIGp(wo+pp,:))),'mo-','LineWidth',2,'MarkerSize',6) +legend('acutal signal power','avg. signal power') +grid on +box on +%} \ No newline at end of file diff --git a/SIMexpt/OTF.tif b/SIMexpt/OTF.tif new file mode 100644 index 0000000000000000000000000000000000000000..424998dc09ef8ed887cc92220569690131e72e05 GIT binary patch literal 524410 zcmcef2izS+_5Sw)Dv0zhy+Z&AAqkx%1PGypP(lwKLhl^}=}nO)y*B}=QbZIH5JW(V z*pVVdQ9%U}RPguzKKtDB&g|a3Zv+3CPu|;iXJ^mzoHA$5j2}Own3lFz+4e5>F7_$* zE%qz+FAgXUEDkCTDGn_TFODpZE{-X_TpVAVP@GhpQk+(tQJhtLt@wIzZgD|zVR3PB 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