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arXiv · 2109.01434

A multi-frequency sampling method for the inverse source problems with sparse measurements

Xiaodong Liu·Shixu Meng
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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 analysed. Motivated by such a factorization, we introduce a multi-frequency sampling method to reconstruct the source support. Its theoretical foundation is then 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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Xiaodong Liu, Shixu Meng. 2021-09-03. A multi-frequency sampling method for the inverse source problems with sparse measurements. https://arxiv.org/abs/2109.01434

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