Fast Algorithms for Multidimensional DCT-to-DCT Computation Between a Block and Its Associated Subblocks.

In this paper, we first propose an efficient algorithm for computing one-dimensional (1-D) discrete cosine transform (DCT) for a signal block, given its two adjacent sub blocks in the DCT domain and then introduce several algorithms for the fast computation of multidimensional (m-D) DCT with size N1 × N2 ×…× Nm given 2m subblocks of DCT coefficients with size N1/2 × N2/2 ×… × Nm/2, where Ni(i=1,2,ߪ,m) are powers of 2. Obviously, the row-column method, which employs the most efficient algorithms along each dimension, reduces the computational complexity considerably, compared with the traditional method, which employs only the one-dimensional (1-D) fast DCT and inverse DCT (IDCT) algorithms. However, when m & 2, the traditional method, which employs the most efficient multidimensional DCT/IDCT algorithms, has lower computational complexity than the row-column method. Besides, we propose a direct method by dividing the data into 2m parts for independent fast computation, in which only two steps of r-dimensional (r = 1,2,…, m) IDCT and additional multiplications and additions are required. If all the dimensional sizes are the same, the number of multiplications required for the direct method is only (2m - 1)/m2m-1 times of that required for the row-column method, and if N & 22m-1, the computational efficiency of the direct method is surely superior to that of the traditional method, which employs the most efficient multidimensional DCT/DCT algorithms. [ABSTRACT FROM AUTHOR]