A general total variation minimization theorem for compressed sensing based interior tomography

Authors:
Weimin Han;Hengyong Yu;Ge Wang
Affiliations:
Department of Mathematics, University of Iowa, Iowa City, IA;Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Sciences, Virginia Tech, Blacksburg, VA;Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Sciences, Virginia Tech, Blacksburg, VA
Venue:
Journal of Biomedical Imaging
Year:
2009

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Abstract

Recently, in the compressed sensing framework we found that a two-dimensional interior region-of-interest (ROI) can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant (Yu and Wang, 2009). Here we present a general theorem charactering a minimization property for a piecewise constant function defined on a domain in any dimension. Our major mathematical tool to prove this result is functional analysis without involving the Dirac delta function, which was heuristically used by Yu and Wang (2009).