Combined polynomial transform and radix-q algorithm for MD discrete W transform

The type-II r-dimensional discrete W transform (rD-DWT-II) with size q/sup l1//spl times/q/sup l2//spl times//spl middot//spl middot//spl middot//spl times//sup lr/ q where q is an odd prime number, is converted into a series of one-dimensional (1-D) reduced DWT-IIs by using the multidimensional polynomial transform and an index permutation. Then, a radix-q algorithm and a cyclic convolution algorithm are presented for the computation of the 1-D reduced DWT-IIs. The new fast algorithm substantially reduces the overall computational complexity compared with the row-column method. Especially, the number of multiplications required by the proposed algorithm for computing an rD-DWT-II is only 1/r times that needed by the commonly used row-column method.