2D discrete cosine transform

Question

I checked with dct function in Matlab but it only implemented DCT along the columns for a matrix input:

>> help dct 
If X is a matrix, the DCT operation is applied to each
column.

Is there a function that can perform 2D DCT in Matlab, or are there some algorithms that can apply dct, make some transform, then obtain the 2D DCT?

Answer 1

According to Wikipedia, "Multidimensional variants of the various DCT types follow straightforwardly from the one-dimensional definitions: they are simply a separable product (equivalently, a composition) of DCTs along each dimension."

Following this, you should be able to get the 2d-DCT by computing

dct(dct(A.').')

There's also dct2 in the Image Processing Toolbox, and the core of the implementation is

b = dct(a, mpad);
if m > 1 && n > 1, b = dct(b.', npad).'; end