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    Improved Wavelet Denoising via Empirical Wiener Filtering

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    Author
    Ghael, Sadeep; Sayeed, Akbar M.; Baraniuk, Richard G.
    Date
    2004-01-08
    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.
    Description
    Conference Paper
    Citation
    S. Ghael, A. M. Sayeed and R. G. Baraniuk, "Improved Wavelet Denoising via Empirical Wiener Filtering," 1997.
    Published Version
    http://dx.doi.org/10.1117/12.292799
    Keyword
    wavelets; denoising; estimation; Wiener filter; subspace; More... Wavelet based Signal/Image Processing; wavelets; denoising; estimation; Wiener filter; subspace Less...
    Type
    Conference paper
    Citable link to this page
    https://hdl.handle.net/1911/19895
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    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map