Journal article
A General Total Variation Minimization Theorem for Compressed Sensing Based Interior Tomography
International journal of biomedical imaging, Vol.2009, pp.125871-3
11/04/2009
DOI: 10.1155/2009/125871
PMCID: PMC2786191
PMID: 20011656
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
- Title: Subtitle
- A General Total Variation Minimization Theorem for Compressed Sensing Based Interior Tomography
- Creators
- Weimin Han - University of IowaHengyong Yu - Virginia TechGe Wang - Virginia Tech
- Contributors
- Guowei Wei (Editor)
- Resource Type
- Journal article
- Publication Details
- International journal of biomedical imaging, Vol.2009, pp.125871-3
- DOI
- 10.1155/2009/125871
- PMID
- 20011656
- PMCID
- PMC2786191
- NLM abbreviation
- Int J Biomed Imaging
- ISSN
- 1687-4188
- eISSN
- 1687-4196
- Publisher
- Hindawi Publishing Corporation
- Grant note
- DOI: 10.13039/100000070, name: National Institute of Biomedical Imaging and Bioengineering, award: EB002667, EB004287, EB007288
- Language
- English
- Date published
- 11/04/2009
- Academic Unit
- Mathematics
- Record Identifier
- 9984240776902771
Metrics
18 Record Views