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

Michael V. Klibanov1; Jingzhi Li2; Loc H. Nguyen1; Vladimir Romanov3; Zhipeng Yang4

2023-08-29

10.1137/23M1565449

SIAM Journal on Imaging Sciences   影响因子和分区

1936-4954

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.

geodesic lines Riemannian metric Carleman estimate coefficient inverse problem global conver-gence convexification numerical studies

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英语

其他

Computer Science ; Mathematics ; Imaging Science & Photographic Technology

Computer Science, Artificial Intelligence ; Computer Science, Software Engineering ; Mathematics, Applied ; Imaging Science & Photographic Technology

WOS:001165602900002

SIAM PUBLICATIONS

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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
4.Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, People's Republic of China

Michael V. Klibanov,Jingzhi Li,Loc H. Nguyen,et al. Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation[J]. SIAM Journal on Imaging Sciences,2023,16(3):1762-1790.

Michael V. Klibanov,Jingzhi Li,Loc H. Nguyen,Vladimir Romanov,&Zhipeng Yang.(2023).Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation.SIAM Journal on Imaging Sciences,16(3),1762-1790.

Michael V. Klibanov,et al."Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation".SIAM Journal on Imaging Sciences 16.3(2023):1762-1790.