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A General Total Variation Minimization Theorem for Compressed Sensing Based Interior Tomography

Authors :
Weimin Han
Hengyong Yu
Ge Wang
Source :
International Journal of Biomedical Imaging, Vol 2009 (2009)
Publication Year :
2009
Publisher :
Hindawi Limited, 2009.

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).

Details

Language :
English
ISSN :
16874188 and 16874196
Volume :
2009
Database :
Directory of Open Access Journals
Journal :
International Journal of Biomedical Imaging
Publication Type :
Academic Journal
Accession number :
edsdoj.14260945112b4d2881c0692cfcd5d9c3
Document Type :
article
Full Text :
https://doi.org/10.1155/2009/125871