CONVERGENCE ANALYSIS OF THE LOPING OS-EM ITERATIVE VERSION OF THE CIRCULAR RADON TRANSFORM

doi:10.1016/S0252-9602(14)60131-4

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (6): 1875-1884.doi: 10.1016/S0252-9602(14)60131-4

CONVERGENCE ANALYSIS OF THE LOPING OS-EM ITERATIVE VERSION OF THE CIRCULAR RADON TRANSFORM

郭娟|王金平*

Faculty of Science, Ningbo University, Ningbo, 315211, China

收稿日期:2013-04-01 修回日期:2013-03-11 出版日期:2014-11-20 发布日期:2014-11-20
通讯作者: 王金平，wangjinping@nbu.edu.cn E-mail:guojuan821@sina.com; wangjinping@nbu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (61271398), K. C.Wong Magna Fund in Ningbo University and Natural Science Foundation of Ningbo City (2010A610102).

CONVERGENCE ANALYSIS OF THE LOPING OS-EM ITERATIVE VERSION OF THE CIRCULAR RADON TRANSFORM

GUO Juan, WANG Jin-Ping*

Faculty of Science, Ningbo University, Ningbo, 315211, China

Received:2013-04-01 Revised:2013-03-11 Online:2014-11-20 Published:2014-11-20
Contact: WANG Jin-Ping，wangjinping@nbu.edu.cn E-mail:guojuan821@sina.com; wangjinping@nbu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (61271398), K. C.Wong Magna Fund in Ningbo University and Natural Science Foundation of Ningbo City (2010A610102).

摘要/Abstract

摘要：

The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transform. We show that the proposed method converges weakly for the noisy data. Numerical tests are presented for a linear problem related to
photoacoustic tomography.

关键词: ill-posed equations, regularization, loping OS-EM iteration, circular Radon transform

Abstract:

Key words: ill-posed equations, regularization, loping OS-EM iteration, circular Radon transform

中图分类号:

44A15

郭娟, 王金平. CONVERGENCE ANALYSIS OF THE LOPING OS-EM ITERATIVE VERSION OF THE CIRCULAR RADON TRANSFORM[J]. 数学物理学报(英文版), 2014, 34(6): 1875-1884.

GUO Juan, WANG Jin-Ping. CONVERGENCE ANALYSIS OF THE LOPING OS-EM ITERATIVE VERSION OF THE CIRCULAR RADON TRANSFORM[J]. Acta mathematica scientia,Series B, 2014, 34(6): 1875-1884.

参考文献

[1] Haltmeier M, Leitao A, Resmerita E. On regularization methods of EM-Kaczmarz type. Inverse Problems, 2009, 25: 075008

[2] Resmerita E, Engl H W, Iusem A N. The expectation-maximization algorithm for ill-posed integral equa-tions: a convergence analysis. Inverse Problems, 2007, 23: 2575–2588

[3] Haltmeier M. Convergence analysis of a block iterative version of the loping Landweber-Kaczmarz iteration. Nonlinear Analysis-Theory, Methods and Applications, 2009, 71: 2912–2919

[4] Borwein J M, Lewis A S. Convergence of the best entropy estimates. SIAM J Optim, 2002, 1: 191–205

[5] Resmerita E, Anderssen R S. Joint additive Kullback-Leibler residual minimization and regularization for linear inverse problems. Math Methods Appl Sci, 2007, 30: 1527–1544

[6] Iusem A N. A short convergence proof of the EM algorithm for a specific Poisson model. Rev Bras Probab Estat, 1992, 6: 57–67

[7] Engl H W, Hanke M, Neubauer A. Regularization of Inverse Problems. Dordrecht: Kluwer Academic Publishers Group, 1996

[8] Bakushinsky A B, Kokurin M Y. Iterative Methods for Approximate Solution of Inverse Problems. Dor-drecht: Springer, 2004

[9] Ambartsoumian G, Gouia-Zarrad, Lewis M. Inversion of the circular Radon transform on annulus. Inverse Problems, 2010, 26: 105015

[10] Ambartsoumian G, Kuchment P. On the injectivity of the circular Radon transform. Inverse Problems, 2005, 21: 473–485

[11] Ambatrsoumian G, Kuchment P. A range description for the planar circular Radon transform. SIAM J Math Anal, 2006, 38: 2681–2692

[12] Wang J P. Inversion and property characterization on generalized transform of Radon type. Acta Math Sci, 2011, 31A(3): 636–643

[13] Shi T T, Wang J P. Reconstruction of the attenuated Radon transform in -scheme short-scan SPECT. Acta Math Sci, 2013, 33B(6): 1615–1626

[14] Hudson H M, Larkin R S. Accelerated image reconstruction using ordered subsets projection data. IEEE Trans Med Imaging, 1994, 13: 601–609

[15] Wang J P, Du J Y. A note on singular value decomposition for Radon transform in Rn. Acta Math Sci, 2002, 22B(3): 311–318

[16] Byrne C. Block-iterative algorithms. Intl Trans Oper Res, 2009, 16: 427–463

[17] Wallis J W, Miller T R. Rapidly converging iterative reconstruction algorithms in Single-Photon Emission Computed Tomography. J Nucl Med, 1993, 34(10): 1793–1800

[18] Yin Y, Liu L. Study of OS-EM with different subsets in fan beam reconstruction. CT Theory Appl, 2003, 12(3): 1–8

CONVERGENCE ANALYSIS OF THE LOPING OS-EM ITERATIVE VERSION OF THE CIRCULAR RADON TRANSFORM

CONVERGENCE ANALYSIS OF THE LOPING OS-EM ITERATIVE VERSION OF THE CIRCULAR RADON TRANSFORM

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 14

Metrics

本文评价

推荐阅读 10

[1]	曹道珉, 彭双阶, 严树森. REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW[J]. 数学物理学报(英文版), 2018, 38(5): 1443-1467.
[2]	Santhosh GEORGE, C. D. SREEDEEP. LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES[J]. 数学物理学报(英文版), 2018, 38(1): 303-314.
[3]	Ioannis K. ARGYROS, Santhosh GEORGE. ITERATIVE REGULARIZATION METHODS FOR NONLINEAR ILL-POSED OPERATOR EQUATIONS WITH M-ACCRETIVE MAPPINGS IN BANACH SPACES[J]. 数学物理学报(英文版), 2015, 35(6): 1318-1324.
[4]	杨帆, 傅初黎, 李晓晓. IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION[J]. 数学物理学报(英文版), 2014, 34(4): 1012-1024.
[5]	彭自嘉, 刘益良. EXISTENCE RESULTS FOR A CLASS OF PSEUDOMONOTONE ELLIPTIC-PARABOLIC INCLUSIONS[J]. 数学物理学报(英文版), 2011, 31(5): 1709-1718.
[6]	刘红, 宋永忠. ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM[J]. 数学物理学报(英文版), 2011, 31(2): 383-398.
[7]	黄小为, 吴传生, 吴笛. A FAST CONVERGENT METHOD OF ITERATED REGULARIZATION[J]. 数学物理学报(英文版), 2009, 29(2): 341-348.
[8]	王吉安; 李景; 刘振海. REGULARIZATION METHODS FOR NONLINEAR ILL-POSED PROBLEMS WITH ACCRETIVE OPERATORS[J]. 数学物理学报(英文版), 2008, 28(1): 141-150.
[9]	钟同德; 陈吕萍. THE PERMUTATION FORMULA OF SINGULAR INTEGRALS WITH BOCHNER-MARTINELLI KERNEL ON STEIN MANIFOLDS[J]. 数学物理学报(英文版), 2006, 26(4): 679-690.
[10]	曾三友, 丁立新, 康立山. A METHOD TO APPROACH OPTIMAL ESTORATION IN IMAGE RESTORATION ROBLEMS WITHOUT NOISE ENERGY NFORMATION[J]. 数学物理学报(英文版), 2003, 23(4): 512-.
[11]	田范基. GROWTH OF RANDOM DIRICHLET SERIES (I)[J]. 数学物理学报(英文版), 2000, 20(3): 390-396.
[12]	侯宗义, 杨宏奇. REGULARIZATION METHOD FOR IMPROVING OPTIMAL CONVERGENCE RATE OF THE REGULARIZED SOLUTION OF ILL-POSED PROBLEMS[J]. 数学物理学报(英文版), 1998, 18(2): 177-185.
[13]	陈宏. ON THE ASYMPTOTIC ORDER OF TIKHONOV REGULARIZATION WITH OPERATORS AND DATA ERROR[J]. 数学物理学报(英文版), 1998, 18(1): 35-44.
[14]	S. Abbasbandy, E. Babolian. AUTOMATIC AUGMENTED GALERKIN ALGORITHMS FOR FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND[J]. 数学物理学报(英文版), 1997, 17(1): 69-84.