Question

Use SVD method to compress and decompress images in the MATLAB.

Compression function. The input is an image file and k. The output is a text file containing the reduced U, V , and the reduced diagonals of ?.

Decompression function. The input is the output of the compression code. The output is an image (you can use imshow for this purpose).

Answer 1

Copy the following code. Enter an integer when promted for input. You can run this program for varous values of reduced vectors.

function svdImg()
global r;
global M;
r=input('Number of vectors for reconstruction');
%Reading input image
img = imread('coins.png');
figure,imshow(img,[]);
title('Original image');
[M,N] =size(img);
%Calling Compression function
[FilePath] = comprSvd(img);
%Decompression Code
recImg = deComprSvd(FilePath);

end
function [FilePath] = comprSvd(img)
%Compression function takes image as input,and produces a txt file as
%output
global r;
%Compute SVD
[U,S,V] = svd(double(img));
%Assign reduced vectors
Ur = U(:,1:r);
Sr = S(1:r,1:r);
Vr = V(:,1:r);
%File name
FilePath = 'coef.txt';
%Writing data file
dlmwrite(FilePath,[Ur;Sr;Vr]);
end
function imgRecon = deComprSvd(inptFilePath)
%Decompression function takes txtfile as input and produces the
%reconstructed image.
global r;
global M;
%Reading txt file
K = dlmread(inptFilePath);
%Assigning reduced vectors
Ur = K(1:M,:);
Sr = K(M+1:M+r,:);
Vr = K(M+r+1:end,:);
%Reconstructing image
imgRecon = Ur*Sr*Vr';
figure,imshow(imgRecon,[]);
title(['Reconstruction with ' num2str(r) ' singular values']);
end

Typical Output:

>> svdImg
Number of vectors for reconstruction30
>>

Output images:

The following are the reconstructed imagese with 50,100

It can be observed that the quality of the reconstructed image is increasing as the number of vectors is increasing