Improved wavelet denoising via empirical wiener filtering

Sandeep P. Ghael, Akbar M. Sayeed, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

193 Scopus citations

Abstract

Wavelet shrinkage is a signal estimation technique that exploits the remarkable abilities of the wavelet transform for signal compression. Wavelet shrinkage using thresholding is asymptotically optimal in a minimax mean-square error (MSE) sense over a variety of smoothness spaces. However, for any given signal, the MSE-optimal processing is achieved by the Wiener filter, which delivers substantially improved performance. In this paper, we develop a new algorithm for wavelet denoising that uses a wavelet shrinkage estimate as a means to design a wavelet-domain Wiener filter. The shrinkage estimate indirectly yields an estimate of the signal subspace that is leveraged into the design of the filter. A peculiar aspect of the algorithm is its use of two wavelet bases: one for the design of the empirical Wiener filter and one for its application. Simulation results show up to a factor of 2 improvement in MSE over wavelet shrinkage, with a corresponding improvement in visual quality of the estimate. Simulations also yield a remarkable observation: whereas shrinkage estimates typically improve performance by trading bias for variance or vice versa, the proposed scheme typically decreases both bias and variance compared to wavelet shrinkage.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Pages389-399
Number of pages11
Volume3169
DOIs
StatePublished - 1997
EventWavelet Applications in Signal and Image Processing V - San Diego, CA, United States
Duration: Jul 30 1997Jul 30 1997

Other

OtherWavelet Applications in Signal and Image Processing V
CountryUnited States
CitySan Diego, CA
Period7/30/977/30/97

Keywords

  • Denoising
  • Estimation
  • Subspace
  • Wavelets
  • Wiener filter

ASJC Scopus subject areas

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

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