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Multidimensional directional filter banks and surfacelets.

Yue M Lu1, Minh N Do

  • 1Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. yuelu@uiuc.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|April 5, 2007
PubMed
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Researchers developed a new directional filter bank (NDFB) for multidimensional signal decomposition. This NDFB system efficiently handles N-dimensional data, enabling advanced analysis and representation of complex signals.

Area of Science:

  • Signal Processing
  • Multidimensional Data Analysis
  • Filter Bank Design

Background:

  • The directional filter bank (DFB) was introduced for 2-D signal decomposition.
  • Extending DFBs to higher dimensions while preserving properties is difficult due to their nonseparable nature.

Purpose of the Study:

  • To propose a novel filter bank system, the N-dimensional directional filter bank (NDFB), for arbitrary N-dimensional signals.
  • To enable efficient directional decomposition and perfect reconstruction in higher dimensions.

Main Methods:

  • A tree-structured construction for the NDFB system.
  • Iterated filter bank with a redundancy factor of N for perfect reconstruction.
  • Iterative refinement of angular resolution through expansion rules.

Related Experiment Videos

Main Results:

  • The NDFB achieves directional decomposition of N-dimensional signals (N>=2).
  • In 3-D, NDFB passbands are pyramid-shaped, tiling the frequency space.
  • Perfect reconstruction is achieved with a redundancy factor of N.

Conclusions:

  • The NDFB offers an efficient solution for directional decomposition in N-dimensional spaces.
  • The surfacelet transform, combining NDFB with a multiscale pyramid, effectively represents surface singularities in multidimensional data.