% test SVD on digital image by doing the SVD on image blocks

clear
clc

I = imread('Peppers.bmp');
I = double(I);

Irec1 = zeros(256);
Irec12 = zeros(256);
Irec123 = zeros(256);
Irec1234 = zeros(256);

for i = 1 : 8 : 249
    for j = 1 : 8 : 249
        temp = I(i:(i+7), j:(j+7));
        [U, S, V] = svd(temp);
        Vtranspose = V';
        
        iter1 = S(1,1)*U(:,1)*Vtranspose(1,:);
        iter2 = S(2,2)*U(:,2)*Vtranspose(2,:);
        iter3 = S(3,3)*U(:,3)*Vtranspose(3,:);
        iter4 = S(4,4)*U(:,4)*V(4,:);

        iter12 = iter1 + iter2;
        iter123 = iter1 + iter2 + iter3;
        iter1234 = iter1 + iter2 + iter3 + iter4;

        Irec1(i:(i+7), j:(j+7)) = iter1;
        Irec12(i:(i+7), j:(j+7)) = iter12;
        Irec123(i:(i+7), j:(j+7)) = iter123;
        Irec1234(i:(i+7), j:(j+7)) = iter1234;
    end
end

subplot(2,2,1), imshow(Irec1,[])
subplot(2,2,2), imshow(Irec12,[])
subplot(2,2,3), imshow(Irec123,[])
subplot(2,2,4), imshow(Irec1234,[])