From ce4f33128345afa1e05a02d8da13ab828ee2fd66 Mon Sep 17 00:00:00 2001 From: Gerhard Reinerth Date: Wed, 11 Oct 2023 08:51:09 +0000 Subject: [PATCH 1/2] Updated README.md --- README.md | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index d72ca79..aad6329 100644 --- a/README.md +++ b/README.md @@ -81,7 +81,13 @@ The compression is set to $c = 0.8$, hence $20$ samples are utilized for the opt All experiments consider different compressions and varying noise corruption.\ The parameters used for the experiments are the default values of the different scripts (`run_mrse, run_ssim`).\ Depending on the experiment either the mean/expected mean root squared error ($E\left[d\right]$) or the mean/expected Structural Similarity Index ($E\left[\overline{SSIM}\right]$) is computed.\ -For $E\left[d\right]$ a low runtimes and a low error is desired. For $E\left[\overline{SSIM}\right]$ a value close to 1 is desired, while also having a low expected runtime. +For $E\left[d\right]$ a low runtimes and a low error is desired. For $E\left[\overline{SSIM}\right]$ a value close to 1 is desired, while also having a low expected runtime. $\overline{SSIM}$ incicates a weighted\ +structural similarity, since a measurement/image might consist of complex numbers. In this case the measurement or image is treated as image with $2$ channels. Then, the Structural Similarity Index is calculated as weighted sum s.t. + +```math +\overline{SSIM} = \frac{1}{2}SSIM\left(\hat{\boldsymbol{X}}_1, \boldsymbol{X}_1\right) + \frac{1}{2}SSIM\left(\hat{\boldsymbol{X}}_2, \boldsymbol{X}_2\right) +``` +Here, $\boldsymbol{X}_i$ represents the original image, $\hat{\boldsymbol{X}}_i$ denotes the reconstructed image on the i-th channel respectively. ### Spatiotemporal Dynamics The formula for generating the spatiotemporal dynamics (taken from [here](https://epubs.siam.org/doi/book/10.1137/1.9781611974508)): From a7bd32b1220783e82320d939d2641058110dae1d Mon Sep 17 00:00:00 2001 From: Gerhard Reinerth Date: Wed, 11 Oct 2023 08:53:18 +0000 Subject: [PATCH 2/2] Updated README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index aad6329..b86fa10 100644 --- a/README.md +++ b/README.md @@ -81,7 +81,7 @@ The compression is set to $c = 0.8$, hence $20$ samples are utilized for the opt All experiments consider different compressions and varying noise corruption.\ The parameters used for the experiments are the default values of the different scripts (`run_mrse, run_ssim`).\ Depending on the experiment either the mean/expected mean root squared error ($E\left[d\right]$) or the mean/expected Structural Similarity Index ($E\left[\overline{SSIM}\right]$) is computed.\ -For $E\left[d\right]$ a low runtimes and a low error is desired. For $E\left[\overline{SSIM}\right]$ a value close to 1 is desired, while also having a low expected runtime. $\overline{SSIM}$ incicates a weighted\ +For $E\left[d\right]$ a low runtimes and a low error is desired. For $E\left[\overline{SSIM}\right]$ a value close to 1 is desired, while also having a low expected runtime. $\overline{SSIM}$ denotes a weighted\ structural similarity, since a measurement/image might consist of complex numbers. In this case the measurement or image is treated as image with $2$ channels. Then, the Structural Similarity Index is calculated as weighted sum s.t. ```math