title: High Order Total Variation Minimization for Interior Tomography.
abstract: Recently, an accurate solution to the interior problem was proposed based on the total variation (TV) minimization, assuming that a region of interest (ROI) is piecewise constant. In this paper, we generalize that assumption to allow a piecewise polynomial ROI, introduce the high order TV (HOT), and prove that an ROI can be accurately reconstructed from projection data associated with x-rays through the ROI through the HOT minimization if the ROI is piecewise polynomial. Then, we verify our theoretical results in numerical simulation.
authors.affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China.
authors.forename: Jiansheng
authors.initials: J
authors.lastname: Yang
authors.forename: Hengyong
authors.initials: H
authors.lastname: Yu
authors.forename: Ming
authors.initials: M
authors.lastname: Jiang
authors.forename: Ge
authors.initials: G
authors.lastname: Wang
references.citation: IEEE Trans Med Imaging. 2003 May;22(5):569-79
references.pmid: 12846426
references.citation: Phys Med Biol. 2004 Sep 7;49(17):3903-23
references.pmid: 15470913
references.citation: Commun Numer Methods Eng. 2009 Jun 1;25(6):693-710
references.pmid: 20160959
references.citation: Int J Biomed Imaging. 2009;2009:125871
references.pmid: 20011656
references.citation: Int J Biomed Imaging. 2006;2006:10427
references.pmid: 23165013
references.citation: Phys Med Biol. 2009 Sep 21;54(18):N425-32
references.pmid: 19717891
references.citation: Med Phys. 2006 Oct;33(10):3640-6
references.pmid: 17089830
references.citation: Phys Med Biol. 2009 May 7;54(9):2791-805
references.pmid: 19369711
references.citation: Inverse Probl. 2008 Sep 12;24(6):65001
references.pmid: 20613970
references.citation: Phys Med Biol. 2008 May 7;53(9):2207-31
references.pmid: 18401067
references.citation: Int J Biomed Imaging. 2007;2007:63634
references.pmid: 18256734
references.citation: Int J Biomed Imaging. 2006;2006:14989
references.pmid: 23165018