What is wrong with my 2D discrete cosine transform?

I have to generalize the DCT transform for an image and have takeb the basic equation off of Wikipedia . To change it to 2D space and then compute its inverse i've followed the provided instructions. However, it seems that the output is wrong and cannot restore the image.

Direct Transform for DCT4 is provided here:

function [transformed] = TCD4Matrix(image)
[rows, columns] = size(image);
transformed = image;

for k1 = 0 : (rows - 1)
    for k2 = 0 : (columns - 1)
        summation = 0;
        for m = 0 : (rows - 1)
            for n = 0 : (columns - 1)
                summation = summation + image(m + 1, n + 1) * cos ( (pi * (k1 + 0.5) * (m + 0.5))/rows ) * cos( (pi * (k2 + 0.5) * (n + 0.5))/columns );
            end
        end
        transformed ( k1 + 1, k2 + 1) = summation;
    end
end

end

DCT4-I is provided below:

function [restored] = iTCD4Matrix(image)
[rows, columns] = size(image);
restored = zeros(rows, columns);

for k1 = 0 : (rows - 1)
    for k2 = 0 : (columns - 1)
        summation = 0;
        for m = 0 : (rows - 1)
            for n = 0 : (columns - 1)
                summation = summation + image(m + 1, n + 1) * cos ( (pi * (k1 + 0.5) * (m + 0.5))/rows ) * cos( (pi * (k2 + 0.5) * (n + 0.5))/columns );
            end
        end
        restored ( k1 + 1, k2 + 1) = 4 * summation / (rows * columns);
    end
end

end

I tried plotting both the result and a scaled version of it and there's no difference.

>> grayImage = rgb2gray(imread('logo.png'));
>> imageTransform = TCD4Matrix(grayImage);
>> imageRestore = iTCD4Matrix(imageTransform);
>> imshow(imageRestore, [0 255])
>> imshow(imageRestore)

Thanks.