A fast algorithm for computing multidimensional DCT on certain small sizes

This paper presents a new algorithm for the fast computation of multidimensional (m-D) discrete cosine transform (DCT) with size N₁×N₂×···×N_m, where N_i is a power of 2 and N_i≤256, by using the tensor product decomposition of the transform matrix. It is shown that the m-D DCT or inverse discrete cosine transform (IDCT) on these small sizes can be computed using only one-dimensional (1-D) DCTs and additions and shifts. If all the dimensional sizes are the same, the total number of multiplications required for the algorithm is only 1/m times of that required for the conventional row-column method. We also introduce approaches for computing scaled DCTs in which the number of multiplications is considerably reduced.