Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/13485
Title: Generalized discrete multiwavelet transform with embedded orthogonal symmetric prefilter bank
Authors: Hsung, TC
Lun, DPK 
Shum, YH
Ho, KC
Keywords: Approximation
Approximation order
Linear-phase paraunitary filterbank
Multiwavelets
OFDM modulation
Orthogonality
Prefilter
Wavelet transforms
Wavelets
Issue Date: 2007
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on signal processing, 2007, v. 55, no. 12, p. 5619-5629 How to cite?
Journal: IEEE transactions on signal processing 
Abstract: Prefilters are generally applied to the discrete multiwavelet transform (DMWT) for processing scalar signals. To fully utilize the benefit offered by DMWT, it is important to have the prefilter designed appropriately so as to preserve the important properties of multiwavelets. To this end, we have recently shown that it is possible to have the prefilter designed to be maximally decimated, yet preserve the linear phase and orthogonal properties as well as the approximation power of 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. It can be very difficult to find a compatible filter bank structure; and in some cases, such filter structure simply does not exist, e.g., for multiwavelets of multiplicity 2. 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, since the prefiltering stage is embedded into DMWT, the computational complexity can be greatly reduced. Experimental results show that an over 20% saving in arithmetic operations can be achieved comparing with the traditional DMWT realizations. Second, the new structure provides additional design freedom that allows the resulting prefilters to be maximally decimated, orthogonal and symmetric even for multiwavelets of low multiplicity. We evaluated the new DMWT structure in terms of computational complexity, energy compaction ratio as well as the compression performance when applying to a VQ based image coding system. Satisfactory results are obtained in all cases comparing with the traditional approaches.
URI: http://hdl.handle.net/10397/13485
ISSN: 1053-587X
EISSN: 1941-0476
DOI: 10.1109/TSP.2007.901650
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