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Improved Wavelet Denoising via Empirical Wiener Filtering

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Title: Improved Wavelet Denoising via Empirical Wiener Filtering
Author: Ghael, Sadeep; Sayeed, Akbar M.; Baraniuk, Richard G.
Type: Conference Paper
Keywords: wavelets; denoising; estimation; Wiener filter; subspace
Citation: S. Ghael, A. M. Sayeed and R. G. Baraniuk,"Improved Wavelet Denoising via Empirical Wiener Filtering," in SPIE Technical Conference on Wavelet Applications in Signal Processing,
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.
Date Published: 1997-07-01

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  • ECE Publications [1032 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.