New algorithm for r-dimensional DCT-II

The paper shows that the type-II r-dimensional discrete cosine transform (rD-DCT-II) of size q^l1×q^l2x...xq ^l1, where r>1 and q is an odd prime number, can be converted into a series of one-dimensional reduced DCT-IIs by using the polynomial transform. The number of multiplications for computing an rD-DCT-II is significantly reduced compared to that needed by the row-column method. The total number of arithmetic operations (additions plus multiplications) needed by the proposed algorithm is also reduced substantially. In addition to the capability of dealing with different dimensional sizes, the proposed algorithm also has a simple computational structure because it requires only the 1D-DCT-II and the polynomial transform