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 proper...

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Detalles Bibliográficos
Autores principales: Han, Weimin, Yu, Hengyong, Wang, Ge
Formato: Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2009
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2786191/
https://www.ncbi.nlm.nih.gov/pubmed/20011656
http://dx.doi.org/10.1155/2009/125871
Descripción
Sumario: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).

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