Error in using waverec2

I have a code below,where i used 2 level decomposition and added noise to image ,wen reconstructing i am not getting original image ,please assist

X = imread('cameraman.tif');

[C,S] = wavedec2(X,2,'haar');

A1 = appcoef2(C,S,'haar',1);
A2 = appcoef2(C,S,'haar',2);

[H1,V1,D1] = detcoef2('all',C,S,1);
[H2,V2,D2] = detcoef2('all',C,S,2);

lev=[A1,H1;V1,D1];

figure('name','One_level_Decomposition','numbertitle','off'), imshow(uint8(lev))
q=[A2,H2;V2,D2];

q1=[q,H1;V1,D1];

figure('name','Two_level_Decomposition','numbertitle','off'), imshow(uint8(q1)),title('Two_level_Decomposition')

J = imnoise(q1,'salt & pepper',0.02);
G=J(:)';

p=waverec2(G,S,'haar')

Answer 1

[Wayne King]

You add noise to the image, then denoise in the wavelet domain, then reconstruct.

Like this:

    load sinsin;
    Y = X + 18*randn(size(X));
    [thr,sorh,keepapp] = ddencmp('den','wv',Y);
    xd = wdencmp('gbl',Y,'sym4',2,thr,sorh,keepapp);
    subplot(221)
    imagesc(X); title('Original Image');
    subplot(222);
    imagesc(Y); title('Noisy Image');
    subplot(223)
    imagesc(xd); title('Denoised Image');

Answer 2

[Wayne King]

Why do you expect that after you have added noise to the coefficients and then inverted the wavelet transform that you would obtain the original image?

That will never happen. The wavelet transform (like the Fourier transform) is an invertible transform. If you modify the coefficients (in the wavelet domain or in the Fourier domain) and then invert the transform, you will end up with a different signal (image).

[kash]

ok wayne is it possible to reconstruct from this variable q1

q1=[q,H1;V1,D1];

Answer 3

[Wayne King]

Yes, but you don't need to use anything other than the C,S vectors

 load woman;
 [C,S] = wavedec2(X,2,'haar');
 Xnew = waverec2(C,S,'haar');
 max(max(abs(X-Xnew)))

You see perfect reconstruction

[kash]

Wayne but i need to do some operation after wavedec2 and then reconstruct and find PSNR,some operation may be ADDING NOISE

[kash]

not perfect reconstruction,nearly 70% is enough

[kash]

SOMETHING LIKE THIS

http://note.sonots.com/SciSoftware/haarwavelet.html

by adding noise