dct and idct

dct.m

clear;
clear all; 

%Read image "Fig2.jpg"
%Image=imread('Fig2.jpg');
Image=imread('cameraman.tif');
imshow(Image)
Block=double(Image(1:8,1:8)); %take the first block as an example
disp("original block")
disp(Block)

function table = Block8_DCT(block)
    table = zeros(8, 8);
    higher_energy_factor = 1;

    for u = 0:7
        for v = 0:7
            if u == 0 && v == 0
                % The single DC component needs to be divided by 4 
                % (Or divided by 2 twice, once for the row, once for the col)
                higher_energy_factor = 1/4; 
            elseif u == 0 || v == 0
                % The other 14 values in row 0 and col 0 are divided by 2
                higher_energy_factor = 1/2;
            else
                % The remaining 49 values get no extra division
                higher_energy_factor = 1;
            end

            % Accumulate the weighted sum over all spatial samples
            total = 0;
            for x = 0:7
                for y = 0:7
                    basis = cos((2*x + 1) * u * pi / 16) * ...
                            cos((2*y + 1) * v * pi / 16);
                    total = total + block(x+1, y+1) * basis;
                end
            end

            table(u+1, v+1) = (1/16) * higher_energy_factor * total;
        end
    end
end
dct_out=Block8_DCT(Block);
disp(dct_out)

function block = Block8_IDCT(dct_out)
    block = zeros(8, 8);

    for x = 0:7
        for y = 0:7

            total = 0;
            for u = 0:7
                for v = 0:7
                    basis = cos((2*x + 1) * u * pi / 16) * ...
                            cos((2*y + 1) * v * pi / 16);
                    total = total + dct_out(u+1, v+1) * basis;
                end
            end

            block(x+1, y+1) = total;
        end
    end
end

out1=Block8_IDCT(dct_out);
disp("Recovered block using my own idct function")
disp(Block - out1)

%{
output:
  1.0e-12 *

   -0.1137    0.0568    0.0284   -0.2274         0   -0.1137   -0.2274    0.1137
    0.0853         0    0.0284   -0.0853    0.0853   -0.0284   -0.1137    0.0284
   -0.0853    0.1421    0.1421   -0.0853    0.0284    0.1421    0.0284    0.1421
   -0.1421   -0.0853         0   -0.1705   -0.0568   -0.1705   -0.0853    0.0284
   -0.0284   -0.0284    0.1705   -0.1137    0.1137         0   -0.0284    0.1421
   -0.0284    0.0284   -0.0284   -0.0853    0.0284    0.0853   -0.0853    0.0853
    0.0284   -0.0568   -0.0284   -0.1990    0.0853   -0.0853   -0.1705   -0.0284
    0.0568    0.1705    0.1421    0.0568    0.1705    0.1705         0    0.1705


Which are very close to zero, meaning that our output is correct!
%}