A Multi-Frequency Sampling Method for the Inverse Source Problems with Sparse Measurements

A Multi-Frequency Sampling Method for the Inverse Source Problems with Sparse Measurements

Year:    2023

Author:    Xiaodong Liu, Shixu Meng

CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 4 : pp. 653–671

Abstract

We consider the inverse source problems with multi-frequency sparse near field measurements. In contrast to the existing near field operator based on the integral over the space variable, a multi-frequency near field operator is introduced based on the integral over the frequency variable. A factorization of this multi-frequency near field operator is further given and analyzed. Based on such a factorization, we introduce a single-receiver multi-frequency sampling method to reconstruct a shell support of the source. Its theoretical foundation is derived from the properties of the factorized operators and a properly chosen point spread function. Numerical examples are provided to illustrate the multi-frequency sampling method with sparse near field measurements. Finally we briefly discuss how to extend the near field case to the far field case.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/csiam-am.SO-2022-0052

CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 4 : pp. 653–671

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Sampling method multi-frequency sparse data inverse source problems.

Author Details

Xiaodong Liu

Shixu Meng