Shakthydoss

Objective:

Is to decompress the image  using SVD (SINGLE VALUE DECOMPOSITION) and study the observation.

Assumption:

Single value decomposition: decompose the bigger matrix into smaller.

Image of size M x N (M cross N) can be consider as bigger matrix and using SVD we can decompose that into further smaller matrix hence decomposing of image is obtained.

Tools used:

Initially I stared with octave (the high-level language primarily intended for numerical computations) and i proceed well but when tried to convert image to double conversion by im2double function I got an error saying unidentified line . This is because octave has a bug in im2double for uint16 images, I found this piece of information from one of community site forum

So now it a time to play with Mat lab instead of octave .

Observation and legends:

I took two type of image for compression. Sizes of the images are 400×400.

1. An image that covers less details of the snap.

2. An image that covers more details of the snap.

I apply svd so as to obtain U,S,V matrix and changed the K values to both of images to study the observation.

when K = 400 80 %
when K = 300 60 %
when K = 250 50%
when k = 150 30%		quality of image changes
when k = 50 10%
when K =25 5 %	quality of image changes
when k = 12.5 2.5 %

Mat lab code :

close all

[A,map]=imread(‘h:cccc.jpg’);

Im2D=im2double(A,’indexed’);

imshow(Im2D,map)

[u,s,v]=svd(Im2D);

C=zeros(size(Im2D));

k=10;     // k values will be changed

for

j=1:k

C=C+s(j,j)*u(:,j)*v(:,j).’;

end

C=floor(C);

imshow(C,map)

k=find(C<1);

C(k)=1;

set(gcf,’Unit’,’inches’,’Paperposition’,[0,0,2,1])

print -djpeg ‘lenak.jpg’

Result

Although both images are of same size with same K values, It has been observed that image that coves less details of snap can be decompressed to larger extend than the image that cover more details of the snap.