DWT image compression using linear algebra

Question

Yasmin Tamimi 2016-6-28

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https://ww2.mathworks.cn/matlabcentral/answers/292637-dwt-image-compression-using-linear-algebra

Hi All,

I'm performing a DWT image compression on the cameraman image according to the following equation: Compressed image = H * original image * H^T; where H is the transformation matrix and H^T is its transpose. The operation can be divided into two steps: the first part (Row = H * original image) computes the row transformation and then (Column = Row*H^T); where the column transformed image is the compressed one.

Original_image = imread('cameraman.tif');

Image_double = im2double(Original_image); % Convert it to double

figure;imshow(Image_double);

n=256;

H = ConstructHaarWaveletTransformationMatrix(n); % Transformation matrix from matlab file exchange

Compressed = H*Image_double*H'; %Haar wavelet transformation

C1 = H*Image_double; % row transformation

C2 = C1*H'; % column transformation

The output from the row transformation gives me values larger than one and smaller than zero, but I still need the range to be between zero and one as the original image. So here's what I did:

C11 = C1 + (-min(C1(:))*ones(n,n)); % shift the values by the minimum

C11 = C11/max(C11(:)); % scale

C22 = C11*H';

Unfortunately when I decompress the image according to the following: Decompressed_image = H' * C22 *H; the image is distorted with 0.0067 ssim.

How I can get back my clear image and remove the distortion/ noise. Shall I perform some sort of filtering or shall I subtract something from the decompressed image?

Thanks a lot in advance.