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Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation Full article

Journal SIAM Journal on Imaging Sciences
ISSN: 1936-4954
Output data Year: 2023, Volume: 16, Number: 3, Pages: 1762-1790 Pages count : 29 DOI: 10.1137/23M1565449
Tags geodesic lines, Riemannian metric, Carleman estimate, coefficient inverse problem, global convergence, convexification, numerical studies
Authors Klibanov Michael V. 1 , Li Jingzhi 2 , Nguyen Loc H. 1 , Romanov Vladimir 3 , Ya Zhipeng 2
Affiliations
1 Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223 USA.
2 Department of Mathematics & National Center for Applied Mathematics Shenzhen & SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen 518055, People’s Republic of China.
3 Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0009

Abstract: The first globally convergent numerical method for a coefficient inverse problem for the Riemannian radiative transfer equation (RRTE) is constructed. This is a version of the so-called convexification method, which has been pursued by this research group for a number of years for some other CIPs for PDEs. Those PDEs are significantly different from the RRTE. The presence of the Carleman weight function in the numerical scheme is the key element which insures the global convergence. Convergence analysis is presented along with the results of numerical experiments, which confirm the theory. RRTE governs the propagation of photons in the diffuse medium in the case when they propagate along geodesic lines between their collisions. Geodesic lines are generated by the spatially variable dielectric constant of the medium.
Cite: Klibanov M.V. , Li J. , Nguyen L.H. , Romanov V. , Ya Z.
Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation
SIAM Journal on Imaging Sciences. 2023. V.16. N3. P.1762-1790. DOI: 10.1137/23M1565449 WOS Scopus РИНЦ OpenAlex
Dates:
Submitted: Apr 13, 2023
Accepted: May 31, 2023
Published online: Aug 29, 2023
Identifiers:
Web of science: WOS:001165602900002
Scopus: 2-s2.0-85175641623
Elibrary: 63113720
OpenAlex: W4386251050
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