A general total variation minimization theorem for compressed sensing based interior tomography.
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).
Han
Weimin
W
Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA.
Yu
Hengyong
H
Wang
Ge
G