OMPmatrix.m

function [X, Supp, x_t] = OMPmatrix(Y, A, B, NumIters)

% 1. Initialization
% ------------------
R = Y;      % Residual
Supp = [];  % Support
t = 1;
A_tag = A';
B_tag = B';
[~,N] = size(A);
[M,~] = size(B);

while t<=NumIters  
    str = ['Iteration #', num2str(t)];
    disp(str);
    
    % 2. Find the two indicies of the support
    % ---------------------------------------

    tmp1 = abs(A_tag*R*B_tag);
    [~,i_vec] = max(tmp1);
    [max_val, j] = max(max(tmp1));
    i = i_vec(j);
    
    % 3. Augment index set
    % --------------------
    Supp(t,2) = j;
    Supp(t,1) = i;
   
    Supp_uniq = unique(Supp, 'rows');
    while(size(Supp_uniq,1)<size(Supp,1))
        %%disp('Support error');
        tmp1(i,j)=0;
        
        [~,i_vec] = max(tmp1);
        [max_val, j] = max(max(tmp1));
        i = i_vec(j);  
        
        Supp(t,2) = j;
        Supp(t,1) = i;
        
        Supp_uniq = unique(Supp, 'rows');
    end
    
    % 4. Find the new signal estimate
    % -------------------------------
    D_t = zeros(t,t);
    d_t = zeros(t,1);
    
    m = 1;
    while m<=t
        r = 1;
        while r<=t
            D_t(m,r) = B(Supp(r,2),:)*B_tag(:,Supp(m,2))*A_tag(Supp(m,1),:)*A(:,Supp(r,1));
            r = r+1;
        end
        m = m+1;
    end
    
    
    p = 1;
    while p<=t
        d_t(p,1) = B(Supp(p,2),:)*Y'*A(:,Supp(p,1));
        p = p+1;
    end
    
    x_t = D_t\d_t;
    
    
    % 5. Compute new residual
    % -----------------------
    tmp2 = 0;
    m = 1;
    while m<=t
        tmp2 = tmp2 + x_t(m)*A(:,Supp(m,1))*B(Supp(m,2),:);
        m = m+1;
    end
    
    R = Y-tmp2;
    
    % 6. Increment t and return to step 2
    % -----------------------------------
    t = t+1;
end

X = zeros(N,M);

p = 1;
while p<=NumIters
    X(Supp(p,1),Supp(p,2)) = x_t(p);
    p = p+1;
end