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International Journal of Biomedical Imaging
Volume 2009 (2009), Article ID 125871, 3 pages
http://dx.doi.org/10.1155/2009/125871
Research Article

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

1Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
2Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Sciences, Virginia Tech, Blacksburg, VA 24061, USA

Received 7 September 2009; Accepted 1 November 2009

Academic Editor: Guowei Wei

Copyright © 2009 Weimin Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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).