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    Wavelet-Domain Regularized Deconvolution for Ill-Conditioned Systems

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    Author
    Neelamani, Ramesh; Choi, Hyeokho; Baraniuk, Richard G.
    Date
    2001-08-27
    Abstract
    We propose a hybrid approach to wavelet-based image deconvolution that comprises Fourier-domain system inversion followed by wavelet-domain noise suppression. In contrast to conventional wavelet-based deconvolution approaches, the algorithm employs a regularized inverse filter, which allows it to operate even when the system is non-invertible. Using a mean-square-error metric, we strike an optimal balance between Fourier-domain regularization that is matched to the system and wavelet-domain regularization that is matched to the input signal. Theoretical analysis reveals that the optimal balance is determined by economics of the input signal wavelet representation and the operator structure. The resultant algorithm is fast, <i>O</i>(<i>N</i>log<sub>2</sub><sup>2</sup><i>N</i>) where N denotes the number of samples, and is well-suited to signals and images with spatially-localized phenomena such as edges. In addition to enjoying asymptotically optimal rates of error decay for some systems, the algorithm also achieves excellent performance at fixed data lengths. In simulations with real data, the algorithm outperforms the conventional LTI Wiener filter and other wavelet-based deconvolution algorithms in terms of both visual quality and MSE performance.
    Description
    Conference Paper
    Citation
    R. Neelamani, H. Choi and R. G. Baraniuk, "Wavelet-Domain Regularized Deconvolution for Ill-Conditioned Systems," vol. 1, 1999.
    Published Version
    http://dx.doi.org/10.1109/ICIP.1999.821598
    Keyword
    Fourier-domain; wavelet-based image deconvolution; Image Processing and Pattern analysis; Wavelet based Signal/Image Processing; Multiscale Methods; More... Fourier-domain; wavelet-based image deconvolution Less...
    Type
    Conference paper
    Citable link to this page
    https://hdl.handle.net/1911/20137
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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