% =========================================================================
% Math 336 - Image Processing - Laboratory 4
%
% Image Restoration (Part 2): SVD and PCA.
% Compute the SVD of Barbara.jpg. Plot the sigularity spectrum. Display the
% reconstructions of Barbara using 5%, 10%, 15% and 20% of the singular
% values.
%
% Marty Kandes
% Computational Science Research Center / Department of Physics
% San Diego State University
% Fall 2008
% -------------------------------------------------------------------------
clear all; close all; clc;                  % Clear Matlab workspace.
F = imread('barbara.jpg');                  % Read in theimage.
F = im2double(F);                           % Convert image to double.
F = mat2gray(F);                            % Normalize grayscale image.
[M,N] = size(F);                            % Get dimensions of image.
[U,S,V] = svd(F,0);                         % Compute the SVD of the image.
SIGMA = diag(S);                            % Compute the sigularity spectrum. 
figure;                                     % Open new figure.
semilogy(SIGMA);                            % Plot signularity spectrum.
R = 51;                                     % Set rank of PCA image.
PCA = zeros(M,N);                           % Preallocate PCA image.
for I = 1:R                                 % Reconstruct the image via
    P = U(:,I);                             % PCA using the SVD components.
    Q = V(:,I);                             % 
    PCA = PCA + SIGMA(I).*P*Q';             %
end;                                        %
figure;                                     % Open new figure.
imshow(PCA);                                % Display PCA recontructed image.
imwrite(PCA,'barbara20.jpg','jpg');          % Write image to file.