Trade-off´s in the computation of mono- and multi-dimensional DCT´s

An overview of some alternative algorithms for one- and two-dimensional DCTs (discrete cosine transforms) is given. Operation counts are derived for typical examples useful in image processing. It is shown that it is possible to generalize the 2-D schemes to 3-D DCTs as well. The result is that a 3-D DCT can be obtained from a 3-D DFT (discrete Fourier transform) of the same size on reals at the cost of permutations and O(3/2N³) multiplications. The scheme involves rotations on eight output points at a time. Improvements through scaling are discussed, and implementation issues (both in hardware and software) are addressed