Fast algorithms for the recursive computation of two-dimensional discrete cosine transform

This paper presents an efficient algorithm for computing the two-dimensional discrete cosine transform (2-D DCT) of size p^r × p^r, where p is a prime. The algorithm decomposes the 2-D DCT outputs into three parts: the first part contains outputs whose indices are both multiples of p and forms a 2-D DCT of size p^r-1 × p^r-1, whereas the remaining outputs are further decomposed into two parts, depending on the summation of their indices. The latter two parts can be reformulated as a set of circular correlation (CC) or skew-circular correlation (SCC) matrix-vector products. Such a decomposition procedure can be repetitively carried out, resulting in a sequence of CC and SCC matrix-vector products. Employing fast algorithms for these CC/SCC operations, we can thus obtain algorithms with minimum multiplicative complexity.