A Generalized Orthogonal Symmetric Prefilter Banks for Discrete Multiwavelet Transforms

Prefilters are generally applied to the discrete multiwavelet transform (DMWT) for processing scalar signals. To fully utilize the benefit given by the multiwavelets, we have recently shown a maximally decimated orthogonal prefilter which preserves the linear phase property and the approximation power of the multiwavelets. However, such design requires the point of symmetry of each channel of the prefilter to match with the scaling functions of the target multiwavelet system. A compatible filter bank structure can be very difficult to find or simply does not exist, e.g. for multiplicity 2 multiwavelets. In this paper, we suggest a new DMWT structure in which the prefilter is combined with the first stage of DMWT. The advantage of the new structure is twofold: First, the computational complexity can be greatly reduced. Second, additional design freedom allows maximally decimated, orthogonal and symmetric prefilters even for low multiplicity. We evaluated the computational complexity and energy compaction capability of the new DMWT structure. Satisfactory results are obtained in comparing with the traditional approaches.