Two-dimensional orthogonal filter banks with directional vanishing moments

Jianping Zhou, Minh N Do

Research output: Contribution to journalConference article

Abstract

We present two-dimensional filter banks with directional vanishing moments. The directional-vanishing-moment condition is crucial for the regularity of directional filter banks. However, it is a challenging task to design orthogonal filter banks with directional vanishing moments. Due to the lack of multidimensional factorization theorems, traditional one-dimensional methods cannot be extended to higher dimensional cases. Kovačević and Vetterli investigated the design of two-dimensional orthogonal filter banks and proposed a set of closed-form solutions called the lattice structure, where the polyphase matrix of the filter bank is characterized with a set of rotation parameters. Orthogonal filter banks with lattice structures have simple implementation. We propose a method of designing orthogonal filter banks with directional vanishing moments based on this lattice structure. The constraint of directional vanishing moments is imposed on the rotation parameters. We find the solutions of rotation parameters have special structure. Based on this structure, we find the closed-form solution for orthogonal filter banks with directional vanishing moments.

Original languageEnglish (US)
Article number59140T
Pages (from-to)1-9
Number of pages9
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume5914
DOIs
StatePublished - Dec 1 2005
EventWavelets XI - San Diego, CA, United States
Duration: Jul 31 2005Aug 3 2005

Fingerprint

Vanishing Moments
Filter Banks
Filter banks
moments
filters
Lattice Structure
Closed-form Solution
Orthogonal Design
Factorization Theorem
Moment Conditions
Factorization
factorization
regularity
High-dimensional
theorems
Regularity

Keywords

  • Directional vanishing moments
  • Filter banks
  • Geometric and directional analysis
  • Lattice structure
  • Multidimensional
  • Nonseparable filter design
  • Orthogonal
  • Polyphase

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Two-dimensional orthogonal filter banks with directional vanishing moments. / Zhou, Jianping; Do, Minh N.

In: Proceedings of SPIE - The International Society for Optical Engineering, Vol. 5914, 59140T, 01.12.2005, p. 1-9.

Research output: Contribution to journalConference article

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