The document applies the discrete cosine transform (DCT) and its inverse (IDCT) to compress and decompress an image. It first applies DCT row-by-row to the image, discards high-frequency DCT coefficients, applies IDCT to reconstruct each row. It then applies DCT column-by-column to the reconstructed image and discards high frequencies, applies IDCT. It calculates the peak signal-to-noise ratio to quantify compression quality and displays the original and reconstructed images.

1. t=cputime;
o = imread('aerialview.jpg');
w = size (o, 2); %identify no of columns in image
samplesEighth = floor(w / 8); % divide column by 8 and round off
ci8 = [];
[x,y,z]=size(o); % identify the dimensions of image
if z==1 % checking z coordinates; if z=1, image is gray
% scale; if z=3,image is rgb
k=1;
for i=1:size(o,1) % all rows
rowDCT = dct(double(o(i,:,k)));
ci8(i,:,k) = idct(rowDCT(1:samplesEighth), w);
end
elseif z==3
for k=1:3 % all color layers: RGB
for i=1:size(o,1) % all rows
rowDCT = dct(double(o(i,:,k))); %picking every row and applying dct on
% every element of the row,after converting it into double for better
% precision
% dct(k)==dct(k,1)--> gives element of 1st row after DCT
% dct(k,2)--> gives element of 2nd row after DCT & so on thus K correspond to
% input matrix and 1 or 2 tells the respective rows on which DCT is to be
applied
% DCT(K(1,3))--> element at 1st row 3rd column of matric K DCT(K(2,5))--
>element at 2nd row 5th column of matric K
ci8(i,:,k) = idct(rowDCT(1:samplesEighth), w);
% row elements from 1:samplesEighth are taken into consideration, rest
% other elements are ignored and using those elements(1:samplesEighth), all
% the possible values of desired row is predicted and placed, thus the no of
% row elements remains same but it is being influenced by lower elements of
% row.
%%%% Each row is Transformed using the DCT, then high-order samples are
%%%% discarded, and the low-order samples are reverse-transformed using IDCT.
end
end
h = size(o, 1); % identify no of rows in image
samplesEighth = floor(h / 8);
ci8f = [];
[x,y,z]=size(o);
if z==1 % check for z coordinate of image i.e rgb component, if image is
% colored, z==3 else z==1 if image is gray
k=1;
for i=1:size(o, 2) % all columns
columnDCT8=dct(double(ci8(:,i,k)));

2. ci8f(:,i,k) = idct(columnDCT8(1:samplesEighth), h);
end
elseif z==3
for k=1:3% all color layers: RGB
for i=1:size(o, 2)% all columns
columnDCT8=dct(double(ci8(:,i,k)));
ci8f(:,i,k) = idct(columnDCT8(1:samplesEighth), h);
end
end
end
k=uint8(ci8f);
figure, imshow(o), title('Original Image');
figure,imshow(k),title('Compression factor 8*8');
out1=uint8(k);
%calculate the peak signal to noise ratio.
input_ima1=double(o);
out2=double(out1);
error=0;
for y=1:191
for x=1:159
MSE=((input_ima1(x,y))-(out2(x,y)))^2;
error=MSE+error;
% error_sbw1=error_sbw+MSE2;
end
end
MSE_WO=(1/(159*191))*error
disp('PSNR value for decompression image using DCT compression ');

3. PSNR_WO=20*log10(255/sqrt(MSE_WO))
%Display the PSNR value.
disp(PSNR_WO);
disp('value for BER ');
BER= 1/PSNR_WO
disp('the time need to execute this program only');
cputime-t