decompressing an compressed image

I have a code for compression please telll how to decompress an image from that compressd image

y=imread('dock.jpg');
y=rgb2gray(y);y=double(y)
threshold=0.125
y=imresize(y,[256 256 ])
low=min(min(y));  high=max(max(y));     % NEEDED LATER FOR DISPLAYING

figure,
imagesc(y), colormap(gray), axis off
title('original image')

w=wavmat;

ty = w'*y*w;                            % THE WAVELET TRANSFORMATION

tty=ty;                                 % A TRICK TO ELIMNATE THE OVERALL
tty(1,1)=0;                             % AVERAGE FROM CONSIDERATION WHEN
dead=max(max(abs(tty)))*threshold/100;  % DECIDING JUST HOW TO THRESHOLD
clear tty;

dy=ty;

index=find(abs(dy)<=dead);
dy(index)=zeros(size(index));           % SETTING LOTS OF ELEMENTS TO ZERO

cy = full(w*sparse(dy)*w');             % THE INVERSE WAVELET TRANSFORMATION

density = nnz(dy);                      % ENTRIES USED OUT OF 256^2 = 65536
disp(['Wavelet transformed and doctored matrix uses '])
disp([ num2str(density) ' entries out of 256^2 = 65536,'])
disp(['thus is ' num2str(100*density/65536) '% dense, and we get a '])
disp(['compression ratio of ' num2str(65536/nnz(dy)) ' to 1'])  % "COMPRESSION RATIO" = 65536/DENSITY

figure,
imagesc(cy,[low high]), colormap(gray), axis off
title('compressed image')

[Jan]

It would be helpful for all readers, if you post the relevant code only.

[shital shinde]

yes. I also need the implimentation of inverse DCT. Its very helpful.

Answer 1

[Wayne King]

I'm not sure what you mean here by decompress, but what you have implemented is lossy compression so you cannot "invert" your process to come up with the exact original image. In other words, you cannot take your cy and reproduce y such that the norm of their difference is zero.

When you execute:

 dy(index)=zeros(size(index))

You have set the wavelet coefficients below a certain level to 0. You no longer know what the value of those coefficients was, so when you invert the wavelet transform, you cannot match your original image.

Now, you could use ty (the wavelet transform of y) and invert that, but that is not a compressed image.

[Pat]

Thanks Wayne for ur comments is there any compression and decompression algorithm where the the compresion ratios are in range 1:2,1:3,1:4

[Walter Roberson]

There is no *possible* lossless compression algorithm which can average better than 1:1 (over a sufficiently large set of inputs.)

*If* you had a program that could _always_ do at least 1:2, then to get 1:4 you would just apply the algorithm twice. If you had an image that was 2 bytes (16 bits) and you applied the hypothetical algorithm 5 times, how would you store the resulting half bit?

To *consistently* get 1:2 or better, you would need to use a lossy compression algorithm.

[Jan]

@Pat: It is not helpful if you ask the same questions repeatedly instead of replying to the questions for clarifications. See: http://www.mathworks.com/matlabcentral/answers/36383-compressing-a-image

and http://www.mathworks.com/matlabcentral/answers/32129-compression-and-decompresion

[Jan]

@Walter: Human tend to prefer images with less than the full entropy. Therefore lossless compressions are possible, if the rounding error are neglected, for a large set of usual pictures. But if a "sufficiently large set" includes random and max-entropy pictures, any 1:1+e compression must be lossless, as you have explained.