On two-channel filter banks with directional vanishing moments

Arthur L. da Cunha, Minh N. Do

Research output: Contribution to journalArticle

Abstract

The contourlet transform was proposed to address the limited directional resolution of the separable wavelet transform. One way to guarantee good approximation behavior is to let the directional filters in the contourlet filter bank have sharp frequency response. This requires filters with large support size. We seek to isolate the key filter property that ensures good approximation. In this direction, we propose filters with directional vanishing moments (DVM). These filters, we show, annihilate information along a given direction. We study two-channel filter banks with DVM filters. We provide conditions under which the design of DVM filter banks is possible. A complete characterization of the product filter is, thus, obtained. We propose a design framework that avoids 2-D factorization using the mapping technique. The filters designed, when used in the contourlet transform, exhibit nonlinear approximation comparable to the conventional filters while being shorter and, therefore, providing better visual quality with less ringing artifacts. Furthermore, experiments show that the proposed filters outperform the conventional ones in image approximation and denoising.

Original languageEnglish (US)
Pages (from-to)1207-1219
Number of pages13
JournalIEEE Transactions on Image Processing
Volume16
Issue number5
DOIs
StatePublished - May 1 2007

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Keywords

  • Biorthogonal filter banks
  • Contourlets
  • Directional vanishing moments (DVM)
  • Multidimensional filter banks
  • Nonlinear approximation
  • Nonseparable filter design

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

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