A polynomial-transform based computation of the 2-D DCT with minimum multiplicative complexity

This paper provides a full description of a 2-D discrete cosine transform (DCT) which has the property of requiring only N 1-D DCT of size N for performing the 2-D algorithm. No multiplication is involved elsewhere in the algorithm, thus the multiplicative complexity is halved when compared to classical row/column algorithms. Compared to some other proposed algorithms, our approach has the characteristic of being formally very concise. Once the main result has been obtained, a remaining difficulty is the search for an in-place algorithm. This problem is also solved.