On the computation of two-dimensional DCT

A new fast algorithm for the type-II two-dimensional (2-D) discrete cosine transform (DCT) is presented. It shows that the 2-D DCT can be decomposed into cosine-cosine, cosine-sine, sine-cosine, and sine-sine sequences that can be further decomposed into a number of similar sequences. Compared with other reported algorithms, the proposed one achieves savings on the number of arithmetic operations and has a recursive computational structure that leads to a simplification of the input/output indexing process. Furthermore, the new algorithm supports transform sizes (p/sub 1/*2/sup m1/)/spl times/(p/sub 2/*2/sup m2/), where p/sub 1/ and p/sub 2/ are arbitrarily odd integers, which provides a wider range of choices on transform sizes for various applications.