i'm a master student ,i have a home work about DCT, i have the code but it does not work ;please help me

i=imread('image065.jpg'); DCT=zeros(8,8); DCT(1:8,1)=1/sqrt(8);

 for p=1:8
     for q=2:8
         DCT(p,q)=1/2 *cos((2*(p-1)+1)*(q-1)*pi/16);
     end
 end
 DCTTRANSP=DCT';

 iR8=zeros(8,8);
 iG8=zeros(8,8);
 iB8=zeros(8,8);

 iRDCT=zeros(128,128);
 iGDCT=zeros(128,128);
 iBDCT=zeros(128,128);

 for p=1:16
     for Q=1:16
         for P=1:8
             for q=1:8
                 iR8(p,q)=i(8*(p-1)+p,8*(Q-1)+q,1);
                 iG8(p,q)=i(8*(p-1)+p,8*(Q-1)+q,2);
                 iB8(p,q)=i(8*(p-1)+p,8*(Q-1)+q,3);
             end
         end
     end
 end  

 iR8DCT=DCTTRANS* iR8* DCT;
 iG8DCT=DCTTRANS* iG8* DCT;
 iB8DCT=DCTTRANS* iB8* DCT;
 for p=1:8
     for q=1:8
         iR8DCT(8*(p-1)+p,  8*(Q-1)+q)=iR8DCT(p,q);
         iG8DCT(8*(p-1)+p,  8*(Q-1)+q)=iG8DCT(p,q);
         iB8DCT(8*(p-1)+p,  8*(Q-1)+q)=iB8DCT(p,q);
     end
 end

 for p=1:16
     for Q=1:16
         for P=1:8
             for q=1:8
                 iR8DCT(p,q)= iRDCT(8*(p-1)+p, 8*(Q-1)+q);
                 iG8DCT(p,q)= iGDCT(8*(p-1)+p, 8*(Q-1)+q);
                 iB8DCT(p,q)= iBDCT(8*(p-1)+p, 8*(Q-1)+q);
             end
         end
         iR8=inv(DCTTRANSP) * iR8DCT * inv(DCT);
         iG8=inv(DCTTRANSP) * iG8DCT * inv(DCT);
         iB8=inv(DCTTRANSP) * iB8DCT * inv(DCT);
         for P=1:8
             for q=1:8
                 iR(8*(p-1)+p,8*(Q-1)+q)=iR8(p,q);
                 iG(8*(p-1)+p,8*(Q-1)+q)=iG8(p,q);
                 iB(8*(p-1)+p,8*(Q-1)+q)=iB8(p,q);
             end 
         end 
     end 
 end
 ip(:,:,1)=iR;
  ip(:,:,2)=iG;
   ip(:,:,3)=iB;
   ip=uint8(ip);
   figure;
   imshow(ip);

Answer 1

[Omega]

Hi Saadi,

I understand that you're encountering issues with the Discrete Cosine Transform (DCT). Here are some issues in your code that need to be addressed:

1. Variable Names: There's a typo with "DCTTRANSP" and "DCTTRANS". Ensure consistency in naming.
2. Indexing: There's a problem with how you're indexing the image. You should use "P" instead of "p" in some places.
3. Inversion: You don't need to manually invert the "DCT" matrix. Use DCT' for the transpose.
4. Output Image Initialization: Make sure to initialize "iR", "iG", and "iB".

You can refer to the corrected code below. Ensure the image is 128x128 pixels; if not, adjust the code or resize the image accordingly.

i = imread('sample_image.jpg'); % replace your image
DCT = zeros(8,8);
DCT(1:8,1) = 1/sqrt(8);
for p = 1:8
    for q = 2:8
        DCT(p,q) = 1/2 * cos((2*(p-1)+1)*(q-1)*pi/16);
    end
end
DCTTRANSP = DCT';

iR8 = zeros(8,8);
iG8 = zeros(8,8);
iB8 = zeros(8,8);

iRDCT = zeros(128,128);
iGDCT = zeros(128,128);
iBDCT = zeros(128,128);

for P = 1:16
    for Q = 1:16
        for p = 1:8
            for q = 1:8
                iR8(p,q) = i(8*(P-1)+p, 8*(Q-1)+q, 1);
                iG8(p,q) = i(8*(P-1)+p, 8*(Q-1)+q, 2);
                iB8(p,q) = i(8*(P-1)+p, 8*(Q-1)+q, 3);
            end
        end
        
        iR8DCT = DCTTRANSP * iR8 * DCT;
        iG8DCT = DCTTRANSP * iG8 * DCT;
        iB8DCT = DCTTRANSP * iB8 * DCT;
        
        for p = 1:8
            for q = 1:8
                iRDCT(8*(P-1)+p, 8*(Q-1)+q) = iR8DCT(p,q);
                iGDCT(8*(P-1)+p, 8*(Q-1)+q) = iG8DCT(p,q);
                iBDCT(8*(P-1)+p, 8*(Q-1)+q) = iB8DCT(p,q);
            end
        end
    end
end

iR = zeros(128, 128);
iG = zeros(128, 128);
iB = zeros(128, 128);

for P = 1:16
    for Q = 1:16
        for p = 1:8
            for q = 1:8
                iR8DCT(p,q) = iRDCT(8*(P-1)+p, 8*(Q-1)+q);
                iG8DCT(p,q) = iGDCT(8*(P-1)+p, 8*(Q-1)+q);
                iB8DCT(p,q) = iBDCT(8*(P-1)+p, 8*(Q-1)+q);
            end
        end
        
        iR8 = DCT * iR8DCT * DCTTRANSP;
        iG8 = DCT * iG8DCT * DCTTRANSP;
        iB8 = DCT * iB8DCT * DCTTRANSP;
        
        for p = 1:8
            for q = 1:8
                iR(8*(P-1)+p, 8*(Q-1)+q) = iR8(p,q);
                iG(8*(P-1)+p, 8*(Q-1)+q) = iG8(p,q);
                iB(8*(P-1)+p, 8*(Q-1)+q) = iB8(p,q);
            end
        end
    end
end

ip(:,:,1) = iR;
ip(:,:,2) = iG;
ip(:,:,3) = iB;
ip = uint8(ip);
figure;
imshow(ip);

I hope it helps!