Multidimensional directional filter banks and surfacelets

Yue M. Lu, Minh N. Do

Research output: Contribution to journalArticle

Abstract

In 1992, Bamberger and Smith proposed the directional filter bank (DFB) for an efficient directional decomposition of 2-D signals. Due to the nonseparable nature of the system, extending the DFB to higher dimensions while still retaining its attractive features is a challenging and previously unsolved problem. We propose a new family of filter banks, named NDFB, that can achieve the directional decomposition of arbitrary N-dimensional (N ≥ 2) signals with a simple and efficient tree-structured construction. In 3-D, the ideal passbands of the proposed NDFB are rectangular-based pyramids radiating out from the origin at different orientations and tiling the entire frequency space. The proposed NDFB achieves perfect reconstruction via an iterated filter bank with a redundancy factor of N in N-D. The angular resolution of the proposed NDFB can be iteratively refined by invoking more levels of decomposition through a simple expansion rule. By combining the NDFB with a new multiscale pyramid, we propose the surfacelet transform, which can be used to efficiently capture and represent surface-like singularities in multidimensional data.

Original languageEnglish (US)
Pages (from-to)918-931
Number of pages14
JournalIEEE Transactions on Image Processing
Volume16
Issue number4
DOIs
StatePublished - Apr 1 2007

Keywords

  • Directional decomposition
  • Directional filter banks (DFBs)
  • Filter design
  • High-dimensional transforms
  • Surfacelets

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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