Home > matlab > Example_weighted_TVDN.m

Example_weighted_TVDN

PURPOSE ^

% Exampled_weighted_TVDN

SYNOPSIS ^

This is a script file.

DESCRIPTION ^

% Exampled_weighted_TVDN
 Example to demonstrate use of TVDN solver when incorporating weights
 (performs one re-weighting of previous solution).

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Exampled_weighted_TVDN
0002 % Example to demonstrate use of TVDN solver when incorporating weights
0003 % (performs one re-weighting of previous solution).
0004 
0005 
0006 %% Clear workspace
0007 clc;
0008 clear;
0009 
0010 %% Define paths
0011 addpath misc/
0012 addpath prox_operators/
0013 
0014 %% Parameters
0015 N = 64;
0016 input_snr = 30; % Noise level (on the measurements)
0017 randn('seed', 1); rand('seed', 1);
0018 
0019 %% Load image
0020 im = phantom(N);
0021 %
0022 figure(1); clf;
0023 subplot(141), imagesc(im); axis image; axis off;
0024 colormap gray; title('Original image'); drawnow;
0025 
0026 %% Create a mask
0027 % Mask
0028 mask = rand(size(im)) < 0.33; ind = find(mask==1);
0029 % Masking matrix (sparse matrix in matlab)
0030 Ma = sparse(1:numel(ind), ind, ones(numel(ind), 1), numel(ind), numel(im));
0031 
0032 %% Measure a few Fourier measurements
0033 
0034 % Composition (Masking o Fourier)
0035 A = @(x) Ma*reshape(fft2(x)/sqrt(numel(im)), numel(x), 1);
0036 At = @(x) ifft2(reshape(Ma'*x(:), size(im))*sqrt(numel(im)));
0037 
0038 % TV sparsity operator
0039 Psit = @(x) x; Psi = Psit;
0040 
0041 % Select 33% of Fourier coefficients
0042 y = A(im);
0043 
0044 % Add Gaussian i.i.d. noise
0045 sigma_noise = 10^(-input_snr/20)*std(im(:));
0046 y = y + (randn(size(y)) + 1i*randn(size(y)))*sigma_noise/sqrt(2);
0047 
0048 % Display the downsampled image
0049 figure(1);
0050 subplot(142); imagesc(real(At(y))); axis image; axis off;
0051 colormap gray; title('Measured image'); drawnow;
0052 
0053 %% Reconstruct with TV
0054 
0055 % Tolerance on noise
0056 epsilon = sqrt(chi2inv(0.99, 2*numel(ind))/2)*sigma_noise;
0057 
0058 % Parameters for TVDN
0059 param.verbose = 1; % Print log or not
0060 param.rel_obj = 1e-4; % Stopping criterion for the TVDN problem
0061 param.max_iter = 200; % Max. nb. of iterations for the TVDN problem
0062 param.gamma = 1e-1; % Converge parameter
0063 param.nu_B2 = 1; % Bound on the norm of the operator A
0064 param.tol_B2 = 1e-4; % Tolerance for the projection onto the L2-ball
0065 param.tight_B2 = 1; % Indicate if A is a tight frame (1) or not (0)
0066 param.max_iter_TV = 500; %
0067 param.zero_weights_flag_TV = 0; %
0068 param.identical_weights_flag_TV = 1; %
0069 
0070 % Solve TVDN problem (without weights)
0071 sol_1 = sopt_mltb_solve_TVDNoA(y, epsilon, A, At, Psi, Psit, param);
0072 
0073 % Show first reconstructed image
0074 figure(1);
0075 subplot(143); imagesc(real(sol_1)); axis image; axis off;
0076 colormap gray; 
0077 title(['First estimate: ', ...
0078     num2str(sopt_mltb_SNR(im, real(sol_1))), 'dB']);
0079 drawnow;
0080 clc;
0081 
0082 %% Re-fine the estimate with weighted TV
0083 % Weights
0084 [param.weights_dx_TV param.weights_dy_TV] = sopt_mltb_gradient_op(real(sol_1));
0085 param.weights_dx_TV = 1./(abs(param.weights_dx_TV)+1e-3);
0086 param.weights_dy_TV = 1./(abs(param.weights_dy_TV)+1e-3);
0087 param.identical_weights_flag_TV = 0;
0088 param.gamma = 1e-3;
0089 
0090 % First reconstruction with weights in the gradient
0091 param.zero_weights_flag_TV = 1;
0092 sol_2 = sopt_mltb_solve_TVDNoA(y, epsilon, A, At, Psi, Psit, param);
0093 % Show second reconstructed image
0094 figure(1);
0095 subplot(144); imagesc(real(sol_2)); axis image; axis off;
0096 colormap gray; 
0097 title(['Second estimate: ', ...
0098     num2str(sopt_mltb_SNR(im, real(sol_2))), 'dB']); 
0099 drawnow;

Generated on Fri 22-Feb-2013 15:54:47 by m2html © 2005