A General Total Variation Minimization Theorem for Compressed Sensing Based Interior Tomography
نویسندگان
چکیده
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).
منابع مشابه
Supplemental analysis on compressed sensing based interior tomography.
Recently, in the compressed sensing framework we proved that an interior ROI can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant. In the proofs, we implicitly utilized the property that if an artifact image assumes a constant value within the ROI, then this constant must be zero. Here we prove this property in the space of square integrable functions.
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عنوان ژورنال:
دوره 2009 شماره
صفحات -
تاریخ انتشار 2009