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Related Experiment Videos

Phase-shifting for nonseparable 2-D Haar wavelets.

Mais Alnasser1, Hassan Foroosh

  • 1Computational Imaging Laboratory, Department of Computer Science, University of Central Florida, Orlando, FL 32816, USA. nasserm@cs.ucf.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|July 1, 2008
PubMed
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This study introduces an efficient method for phase-shifting 2-D nonseparable Haar wavelet coefficients. The new approach accurately relates shifted and unshifted coefficients, outperforming traditional interpolation techniques in minimizing error accumulation.

Area of Science:

  • Signal Processing
  • Image Analysis
  • Wavelet Theory

Background:

  • 2-D nonseparable Haar wavelets lack shift-invariance, complicating signal processing tasks.
  • Existing solutions often involve modifying wavelets or introducing new ones, which can be inefficient.
  • Accurate handling of shifted signals is crucial for applications like image registration and analysis.

Purpose of the Study:

  • To present a novel and efficient method for phase-shifting 2-D nonseparable Haar wavelet coefficients.
  • To derive explicit relationships between shifted and unshifted wavelet coefficients.
  • To demonstrate the superiority of the proposed method over classical interpolation tools.

Main Methods:

  • Derivation of explicit mathematical relationships between coefficients of shifted and unshifted signals.

Related Experiment Videos

  • Analysis of the computational complexity of the proposed method.
  • Comparative performance evaluation against classical interpolation techniques using error accumulation metrics.

    • Main Results:

    • The proposed method establishes explicit relationships for phase-shifting 2-D nonseparable Haar wavelet coefficients.
    • The computational complexity of the new approach is analyzed.
    • Demonstrated superior performance in reducing error accumulation compared to classical interpolation methods under successive shifting.

    Conclusions:

    • The novel method provides an efficient and accurate solution for phase-shifting 2-D nonseparable Haar wavelet coefficients.
    • The derived relationships offer a significant advantage over existing approaches by avoiding wavelet modification.
    • The findings highlight the potential of this method for improved accuracy in signal processing applications sensitive to shifts.