MATLAB Codes of JPEG Image Compression for Gray-level Image

 Matlab Codes： 

 function JPEG_Compressor (filename,quant_multiple)% JPEG image compression program for graylevel image only% This program compresses a graylevel image using the JPEG algorithm% Parameter:% -- filename, e.g. filename = 'D:\tigerGraylevel.jpg';% -- quant_multiple, i.e.,set the multiplier to change size of quant. levels,and vary quant_mult from 0.1 to 3 (see jpeg.results file)%%%{ [X, map] = imread(...) reads the indexedimage in filename into X andits associated colormap into map. % Colormap valuesin the image file are automatically rescaled into the range [0,1]. }orig_img = imread(filename);          % image matrix was stored in variable X                       % image colormap is stored in variable map                        orig_img = double(orig_img); %Convert image to double precision which is needed for the following calculationsblocksize = 8;         % set the size of chunks to take the DCT of ( =< 8)DCT_quantizer = ...    % levels for quantizing the DCT block (8x8 matrix)[ 16  11  10  16  24  40  51  61; ...  12  12  14  19  26  58  60  55; ...  14  13  16  24  40  57  69  56; ...  14  17  22  29  51  87  80  62; ...  18  22  37  56  68 109 103  77; ...  24  35  55  64  81 104 113  92; ...  49  64  78  87 103 121 120 101; ...  72  92  95  98 112 100 103  99 ];[rows, cols] = size(orig_img); % finds image's rows and columnscolors = max(max(orig_img));  % find the maximum intensity value in the original image% Introductionstr = char( ...  'CpE 645 Image Processin Final Project Changjiang Cai', ...  'This program implements the JPEG data compression algorithm.');ssdisp(0, str);%{fprintf(fileID,formatSpec,A1,...,An) appliesthe formatSpec to all elements of arrays A1,...An,in column order, and writes the data to a text file. fprintf uses the encoding scheme specified in the call to fopen%}fprintf (1, 'Image used:               %s\n', filename);fprintf (1, 'Its size is:              %dx%d\n', rows, cols);fprintf (1, 'Number of colors (guess): %d\n', colors);fprintf (1, 'DCT block size:           %dx%d\n', blocksize, blocksize);fprintf (1, 'Quant. size multiplier:   %d\n', quant_multiple);% Display the original imagefigureax(1) = subplot(1,2,1);image(orig_img)title('Original image')% Prepare image for transform% Level-shift the image (center intensity values around 0)% {B = ceil(A) rounds the elements of A to the nearest integers greater thanor equal to A. % For complex A,the imaginary and real parts are rounded independently.}orig_img = orig_img - ceil(colors/2);% Replicate edges of image to make its dimensions a multiple of blocksize% {B = floor(A) rounds the elements of A to the nearest integers less thanor equal to A. % For complex A,the imaginary and real parts are rounded independently.}% the number of coloums to be paddedpad_cols = (1 - (cols/blocksize - floor(cols/blocksize))) * blocksize; % the above formula may produce this result: when cols = 8, blocksize = 8,then pad_cols = 8% thus, if this case happens, we have to make pad_cols be 0, compulsively.  if pad_cols == blocksize, pad_cols = 0; end% the number of rows to be paddedpad_rows = (1 - (rows/blocksize - floor(rows/blocksize))) * blocksize;if pad_rows == blocksize, pad_rows = 0; end% duplicate the last column for padding new columnsfor extra_cols = 1:pad_cols  orig_img(1:rows, cols+extra_cols) = orig_img(1:rows, cols);endcols = cols + pad_cols;    % orig_img is now pad_cols wider% duplicate the last row for padding new rowsfor extra_rows = 1:pad_rows  orig_img(rows+extra_rows, 1:cols) = orig_img(rows, 1:cols);endrows = rows + pad_rows;    % orig_img is now pad_rows taller% the 1-D DCT transform matrixDCT_trans = dctmtx(blocksize);% Take DCT of blocks of size blocksizefprintf(1, '\nFinding the DCT and quantizing...\n');starttime = cputime;              % "cputime" is an internal cpu time counterjpeg_img = orig_img - orig_img;   % zero the matrix for the compressed imagefor row = 1: blocksize: rows-blocksize+1  for col = 1: blocksize: cols-blocksize+1       % take a block of the image:    DCT_matrix = orig_img(row: row + blocksize-1, col: col + blocksize-1);       % perform the transform operation on the 2-D block    DCT_matrix = DCT_trans*DCT_matrix*DCT_trans';       % quantize it (levels stored in DCT_quantizer matrix):    DCT_matrix = floor (DCT_matrix ...          ./ (DCT_quantizer(1:blocksize, 1:blocksize) * quant_multiple) + 0.5);       % place it into the compressed-image matrix:    jpeg_img(row: row + blocksize-1, col: col + blocksize-1) = DCT_matrix;  endendfprintf(1, ' CPU time used: %1.3f\n', (cputime - starttime))% Reverse the process (take the Inverse DCT)fprintf(1, 'Reconstructing quantized values and taking the inverse DCT...\n');starttime = cputime;recon_img = orig_img - orig_img;  % zero the matrix for the reconstructed imagefor row = 1: blocksize: rows-blocksize+1  for col = 1: blocksize: cols-blocksize+1       % take a block of the image:    IDCT_matrix = jpeg_img(row: row + blocksize-1, col: col + blocksize-1);       % reconstruct the quantized values:    IDCT_matrix = IDCT_matrix ...                .* (DCT_quantizer(1:blocksize, 1:blocksize) * quant_multiple);       % perform the inverse DCT:    IDCT_matrix = DCT_trans' * IDCT_matrix * DCT_trans;       % place it into the reconstructed image:    recon_img(row: row + blocksize-1, col: col + blocksize-1) = IDCT_matrix;  endendfprintf(1, '   CPU time used: %1.3f\n', (cputime - starttime))% Restore image to normal% Level-shift the image backrecon_img = recon_img + ceil(colors/2);orig_img = orig_img + ceil(colors/2);% Clip off padded rows and columnsrows = rows - pad_rows;cols = cols - pad_cols;orig_img = orig_img(1:rows, 1:cols);recon_img = recon_img(1:rows, 1:cols);% Display imageax(2) = subplot(1,2,2);image(recon_img)title('Decompressed JPEG image')linkaxes(ax,'xy')axis(ax,'image')% Calculate the root-mean-square errorfprintf(1, 'Calculate the root-mean-square error...\n');error = orig_img -recon_img;e = reshape(error,1,[]);e_rms = sqrt((e*e')/64);fprintf(1, '\nThe root-mean-square error (RMSE) is: %1.3f\n\n', e_rms);% Calculate signal-to-noise ratiofprintf(1, 'Finding the signal-to-noise ratio...\n');starttime = cputime;PSNR = 0; % Peak-Signal-to-Noise Ratio of the reconstructed imagefor row = 1:rows  for col = 1:cols    PSNR = PSNR + (orig_img(row, col) - recon_img(row, col)) ^ 2;  endendPSNR = 10 * log10 ((255^2) / (1 / (((rows + cols) / 2) ^ 2) * PSNR));             % (averaged rows and cols together)fprintf(1, '   CPU time used: %1.3f\n', (cputime - starttime))fprintf(1, '\nThe signal-to-noise ratio (PSNR) is: %1.3f dB\n\n', PSNR);  end