initial commit

tomo/utils/TV_Fourier_smoothing.m

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+function [recon_constrained] = TV_Fourier_smoothing(I, I_f, Niter, show_figure)
+%UNTITLED3 Summary of this function goes here
+%   Detailed explanation goes here
+%Convergence Parameters
+%Niter = 10;
+iter_TVdecent = 30; 
+a = 0.5; %Decent Parameter
+
+% Create a mask that will remove the region of interest (ROI). 
+mask = I_f~=0;
+
+%Create Random Image
+[nx, ny] = size(I);
+recon_init = rand(nx,ny);
+
+%recon_init = I;
+
+%% 
+for i = 1:Niter
+    
+    % Counter. 
+    disp(i)
+          
+    % FFT of Reconstructed Image.
+    FFTr = fftshift(fft2(ifftshift(recon_init))); 
+    
+    % Remove the ROI with Data Constraint. 
+    FFTr(mask) = I_f(mask);
+ 
+    %Inverse FFT
+    recon_constrained = real(fftshift(ifft2(ifftshift(FFTr))));
+    
+    %Positivity Constraint.
+    %recon_constrained(recon_constrained<0) = 0;
+
+    %TV Minimization. 
+    recon_minTV = recon_constrained;
+    d = (sum(sum((recon_minTV-recon_init).^2))).^(1/2);
+    for j = 1:iter_TVdecent
+
+        Vst = TVDerivative(recon_minTV);
+        L2norm = (sum(sum(Vst.^2))).^(1/2); 
+        Vst = Vst/L2norm;
+        recon_minTV = recon_minTV - a*d*Vst;
+
+    end
+
+    % Initialize next loop. 
+    recon_init = recon_minTV;
+    
+end
+if show_figure
+    % Show the Reconstruction
+    figure
+    imagesc((recon_minTV+recon_constrained)/2); axis image; colormap gray
+    figure
+    f = fftshift(fft2(recon_constrained));
+    imagesc(abs(f).^0.2); axis image; colormap jet
+end
+%Save the Reconstructions
+%imwrite(mat2gray(recon_constrained), [fname '_Reconstruction.tif'], 'tiff') 
+
+end
+