Inverse source problems in an inhomogeneous medium with a single far-field pattern

Hu，Guanghui1; Li，Jingzhi2

2020

10.1137/20M1325289

SIAM JOURNAL ON MATHEMATICAL ANALYSIS   影响因子和分区

0036-1410

1095-7154

This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source terms, we prove that the source support together with the zeroth and first-order derivatives of the source function at corner points can be uniquely determined. Further, we prove that an admissible set of source functions (including harmonic functions) having a convex-polygonal support can be uniquely identified by a single far-field pattern. A class of radiating sources is characterized, and the extension of the radiated field across a corner point is proven impossible. Finally, the corner scattering theory motivates us to design a data-driven inversion scheme for imaging a convex polygonal source support.

Helmholtz equation Inverse source problem Single measurement Uniqueness

SCI ; EI

英语

通讯

National Natural Science Foundation of China[11971221][11731006] ; Shenzhen Sci-Tech Fund grant[JCYJ20190809150413261]

Mathematics

Mathematics, Applied

WOS:000584712300032

SIAM PUBLICATIONS

20204609491255

Inverse problems

Mathematics:921

MATHEMATICS

2-s2.0-85095914904

Scopus

1.School of Mathematical Sciences,Nankai University,Tianjin,300071,China
2.Department of Mathematics,Southern University of Science and Technology (SUSTech),Shenzhen,518005,China

Hu，Guanghui,Li，Jingzhi. Inverse source problems in an inhomogeneous medium with a single far-field pattern[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2020,52(5):5213-5231.

Hu，Guanghui,&Li，Jingzhi.(2020).Inverse source problems in an inhomogeneous medium with a single far-field pattern.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,52(5),5213-5231.

Hu，Guanghui,et al."Inverse source problems in an inhomogeneous medium with a single far-field pattern".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 52.5(2020):5213-5231.