Unitary image transforms and their implementation

The authors analyze the discrete wavelet transform (DWT) and the discrete multiwavelet transform (DMWT) and compare them with the Karhunen-Loeve transform (KLT), the discrete cosine transform (DCT), the Haar transform, and the Hadamard transform. The comparison is made with respect to computational complexity, base construction, energy compaction, and implementational aspects. It is shown that wavelet transforms achieve a compaction performance which is comparable to DCT, whereas they require significantly less computational effort, (O(n²)) instead of O(n ² log n). A VLSI implementation of the DMWT offers the advantage that it can be used for base construction