alinea b

image = imread('img_blackwhite_e2.jpg');
%image = rgb2gray(image);
A=im2double(image);
[U,S,V] = svd(A);
singular_values = diag(S);
singular_values_quantity = length(singular_values);
sum_total_singular_values_squares = sum(singular_values.^2);

preserved_quantities = [25 50 75];
for n = 1 : length(preserved_quantities)
    preserved_quantity = preserved_quantities(n);
    singular_values_length = round(singular_values_quantity*(preserved_quantity/100));
    [U_2,S_2,V_2] = svds(A,singular_values_length);
    singular_values = diag(S_2);
    sum_singular_values_squares = sum(singular_values.^2);
    fprintf('Percentagem de qualidade de dados preservada com %d%% dos valores singulares: %0.8f%% \r\n',preserved_quantity, 100*(sum_singular_values_squares/sum_total_singular_values_squares));
    %Apresentação das imagens com redução dos valores singulares 
    A_2 = U_2*S_2*V_2';
    image_2 = uint8(A_2);
    if(n == 1)
        image_25 = image_2;
    elseif (n==2)
        image_50 = image_2;
    else
        image_75 = image_2;
    end
end


subplot(2,2,1), imshow(image)
title('Imagem original') 
subplot(2,2,2), imshow(image_25)
title('25%') 
subplot(2,2,3), imshow(image_50)
title('50%') 
subplot(2,2,4), imshow(image_75)
title('75%')