On the realization of generalized discrete multiwavelet transforms

One of the major problems of the discrete multiwavelet transform is its high computational complexity. It stems from the use of the matrix-based multifilters and the extra pre and postfiltering stages, which are popularly adopted for initializing the input data. Recently, we proposed a generalized structure for the discrete multiwavelet transform (GDMWT). The new structure allows the prefilters to embed into the transform such that the related complexity of implementing the prefilters can be reduced. In this paper, we further consider the efficient realization method of GDMWT. We show that the matrix-based multifilters can be simplified by applying different Givens rotations to the factorized matrices. A new lattice structure is then proposed for their efficient realizations. As compared with the scalar wavelet transform for example using biorthogonal 9/7 wavelet, the proposed approach has a similar complexity while enjoying a better energy compaction performance.