2-D discrete cosine transform
B = dct2(A)
B = dct2(A,m,n)
B = dct2(A,[m n])
The commands below compute the discrete cosine transform for the autumn image. Notice that most of the energy is in the upper left corner.
RGB = imread('autumn.tif'); I = rgb2gray(RGB); J = dct2(I); imshow(log(abs(J)),), colormap(jet(64)), colorbar
Now set values less than magnitude 10 in the DCT matrix to zero, and then reconstruct the image using the inverse DCT function idct2.
J(abs(J) < 10) = 0; K = idct2(J); imshow(I) figure, imshow(K,[0 255])
The discrete cosine transform (DCT) is closely related to the discrete Fourier transform. It is a separable linear transformation; that is, the two-dimensional transform is equivalent to a one-dimensional DCT performed along a single dimension followed by a one-dimensional DCT in the other dimension. The definition of the two-dimensional DCT for an input image A and output image B is
M and N are the row and column size of A, respectively. If you apply the DCT to real data, the result is also real. The DCT tends to concentrate information, making it useful for image compression applications.
This transform can be inverted using idct2.
 Jain, Anil K., Fundamentals of Digital Image Processing, Englewood Cliffs, NJ, Prentice Hall, 1989, pp. 150-153.
 Pennebaker, William B., and Joan L. Mitchell, JPEG: Still Image Data Compression Standard, Van Nostrand Reinhold, 1993.