A fast 4×4 DCT algorithm for the recursive 2-D DCT

The authors present an efficient algorithm for the computation of the 4×4 discrete cosine transform (DCT). The algorithm is based on the decomposition of the 4×4 DCT into four 4-point 1-D DCTs. Thus, only 1-D transformations and some additions are required. It is shown that the proposed algorithm requires only 16 multiplications, which is half the number needed for the conventional row-column method. Since the 2^m×2^m DCT can be computed using the 4×4 DCT recursively for any m, the proposed algorithm leads to a fast algorithm for the computation of the 2-D DCT