Generalized discrete multiwavelet transform with embedded orthogonal symmetric prefilter bank

Tai Chiu Hsung, Pak Kong Lun, Yu Hing Shum, K. C. Ho

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)5619-5629
Number of pages11
JournalIEEE Transactions on Signal Processing
Volume55
Issue number12
DOIs
Publication statusPublished - 1 Dec 2007

Keywords

  • Approximation
  • Approximation order
  • Linear-phase paraunitary filterbank
  • Multiwavelets
  • OFDM modulation
  • Orthogonality
  • Prefilter
  • Wavelet transforms
  • Wavelets

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

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