A Multiscale Bayesian Framework for Linear Inverse Problems and Its Application to Image Restoration

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dc.citation.bibtexNamearticleen_US
dc.citation.journalTitleIEEE Transactions on Image Processingen_US
dc.contributor.authorWan, Yien_US
dc.contributor.authorNowak, Robert Daviden_US
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)en_US
dc.date.accessioned2007-10-31T01:09:23Z
dc.date.available2007-10-31T01:09:23Z
dc.date.issued2001-01-20en
dc.date.modified2001-10-07en_US
dc.date.submitted2001-10-07en_US
dc.descriptionJournal Paperen_US
dc.description.abstractIn this paper we develop a wavelet-based statistical method for solving linear inverse problems. The Bayesian framework developed here is general enough to treat a wide class of linear inverse problems involving (white or colored) Gaussian observation noise. In this approach, a signal prior is developed by modeling the signal/imgage wavelet coefficients as independent Gaussian mixture random variabls. We first specify a uniform (non-informative) distribution on the mixing parameters, which leads to a simple and efficient iterative algorithm for MAP estimation. This algorithm is similar to the EM algorithm in that it alternates between a state estimation step and a maximization step. Moreover, we show that our algorithm converges monotonically to a local maximum of the posterior distribution. We next generalize the result to non-uniform priors and develop an efficient integer programming algorithm that enables a similar alternating optimization procedure. Experimental reults show that this new method outperforms recent results, including multiscale Kalman filtering and wavelet-vaguelette type methods based on linear inverse filtering followed by wavelet coefficient denoising.en_US
dc.description.sponsorshipOffice of Naval Researchen_US
dc.description.sponsorshipArmy Research Officeen_US
dc.description.sponsorshipNational Science Foundationen_US
dc.identifier.citationY. Wan and R. D. Nowak, "A Multiscale Bayesian Framework for Linear Inverse Problems and Its Application to Image Restoration," <i>IEEE Transactions on Image Processing,</i> 2001.
dc.identifier.urihttps://hdl.handle.net/1911/20439
dc.language.isoeng
dc.subjectbayesian*
dc.subjectimage restoration*
dc.subjectwavelet*
dc.subjectGaussian*
dc.subjectKalman filtering*
dc.subject.keywordbayesianen_US
dc.subject.keywordimage restorationen_US
dc.subject.keywordwaveleten_US
dc.subject.keywordGaussianen_US
dc.subject.keywordKalman filteringen_US
dc.titleA Multiscale Bayesian Framework for Linear Inverse Problems and Its Application to Image Restorationen_US
dc.typeJournal article
dc.type.dcmiText
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