New algorithm for multidimensional type-III DCT

New algorithms are proposed for the type-III multidimensional discrete cosine transform (MD-DCT-III). The polynomial transform is used to convert the type-III MD-DCT into a series of one-dimensional type-III discrete cosine transforms (1-D-DCT-III). The algorithms achieve considerable savings on the number of operations compared to the row column method. For computing an r-dimensional DCT-III, the number of multiplications required by the proposed algorithm is only 1/τ times that needed by the row-column method, and the number of additions is also reduced. Compared to other known fast algorithms for two-dimensional- and MD-DCTs, the proposed method uses about the same number of operations. However, advantages such as better computational structure and flexibility on the choice of dimensional sizes can be achieved