A Multi-Frequency Sampling Method for the Inverse Source Problems with Sparse Measurements (CSIAM Transactions on Applied Mathematics, 2023)
We consider the inverse source problems with multi-frequency sparse nearfield 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 basedon the integral over the frequency variable. A factorization of this multi-frequencynear field operator is further given and analyzed. Based on such a factorization, weintroduce a single-receiver multi-frequency sampling method to reconstruct a shellsupport of the source. Its theoretical foundation is derived from the properties of thefactorized operators and a properly chosen point spread function. Numerical examples are provided to illustrate the multi-frequency sampling method with sparse nearfield measurements. Finally we briefly discuss how to extend the near field case to thefar field case.