It is well known that the diffusion based inverse problem in optical tomography is exponentially ill-posed or unstable, see [2, 18]. In our paper we propose new iteratively regularized numerical methods for the above inverse problem. For the 1D case we compare those methods to MATLAB Levenberg—Marquardt trust region nonlinear least square routine LSQNONLIN both in terms of accuracy and efficiency.
Editor-in-Chief: Kabanikhin, Sergey I.
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Inverse problem in optical tomography and its numerical investigation by iteratively regularized methods
∗Institute of System Analysis, Russian Academy of Sciencies, 117312, Moscow, Russia. E-mail: bakush@isa.ru
†Dept of Mathematical Sciencies, Clemson University, SC 29634, Clemson, USA. E-mail: khan@clemson.edu
‡Dept of Mathematics and Statistics, Georgia State University, GA 30303, Atlanta, USA. E-mail: smirn@mathstat.gsu.edu
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 13, Issue 6, Pages 537–551, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939405775199479,
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