A Multi-Frequency Sampling Method for the Inverse Source Problems with Sparse Measurements
Xiaodong Liu, Shixu Meng
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Source: Crossref
Published: Oct 26, 2023
DOI: 10.4208/csiam-am.so-2022-0052
Open original source ↗Source 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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