ForWaRD: Fourier-Wavelet Regularized Deconvolution for Ill-Conditioned Systems

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dc.citation.bibtexNamearticleen_US
dc.citation.firstpage418
dc.citation.issueNumber2en_US
dc.citation.journalTitleIEEE Transactions on Signal Processingen_US
dc.citation.lastpage433
dc.citation.volumeNumber52en_US
dc.contributor.authorNeelamani, Rameshen_US
dc.contributor.authorChoi, Hyeokhoen_US
dc.contributor.authorBaraniuk, Richard G.en_US
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)en_US
dc.date.accessioned2007-10-31T00:55:37Z
dc.date.available2007-10-31T00:55:37Z
dc.date.issued2004-02-01en
dc.date.modified2006-06-05en_US
dc.date.submitted2002-10-02en_US
dc.descriptionJournal Paperen_US
dc.description.abstractWe propose an efficient, hybrid <i>Fourier-Wavelet Regularized Deconvolution</i> (ForWaRD) algorithm that performs noise regularization via scalar shrinkage in both the Fourier and wavelet domains. The Fourier shrinkage exploits the Fourier transform's sparse representation of the colored noise inherent in deconvolution, while the wavelet shrinkage exploits the wavelet domain's sparse representation of piecewise smooth signals and images. We derive the optimal balance between the amount of Fourier and wavelet regularization by optimizing an approximate mean-squared-error (MSE) metric and find that signals with sparser wavelet representations require less Fourier shrinkage. ForWaRD is applicable to all ill-conditioned deconvolution problems, unlike the purely wavelet-based <i>Wavelet-Vaguelette Deconvolution</i> (WVD), and its estimate features minimal ringing, unlike purely Fourier-based Wiener deconvolution. We analyze ForWaRD's MSE decay rate as the number of samples increases and demonstrate its improved performance compared to the optimal WVD over a wide range of practical sample-lengths.en_US
dc.description.sponsorshipOffice of Naval Researchen_US
dc.description.sponsorshipNational Science Foundationen_US
dc.description.sponsorshipAir Force Office of Scientific Researchen_US
dc.identifier.citationR. Neelamani, H. Choi and R. G. Baraniuk, "ForWaRD: Fourier-Wavelet Regularized Deconvolution for Ill-Conditioned Systems," <i>IEEE Transactions on Signal Processing,</i> vol. 52, no. 2, 2004.
dc.identifier.doihttp://dx.doi.org/10.1109/TSP.2003.821103en_US
dc.identifier.urihttps://hdl.handle.net/1911/20143
dc.language.isoeng
dc.relation.projecthttp://www.dsp.rice.edu/software/ward_abs.shtmlen_US
dc.relation.softwarehttp://www.dsp.rice.edu/software/ward.shtmlen_US
dc.subjectdeconvolution*
dc.subjectrestoration*
dc.subjectdeblurring*
dc.subjectwavelets*
dc.subjectwavelet-vaguelette*
dc.subject.keyworddeconvolutionen_US
dc.subject.keywordrestorationen_US
dc.subject.keyworddeblurringen_US
dc.subject.keywordwaveletsen_US
dc.subject.keywordwavelet-vagueletteen_US
dc.subject.otherImage Processing and Pattern analysisen_US
dc.subject.otherWavelet based Signal/Image Processingen_US
dc.titleForWaRD: Fourier-Wavelet Regularized Deconvolution for Ill-Conditioned Systemsen_US
dc.typeJournal article
dc.type.dcmiText
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