TY - JOUR
T1 - A Multi-Frequency Sampling Method for the Inverse Source Problems with Sparse Measurements
AU - Liu , Xiaodong
AU - Meng , Shixu
JO - CSIAM Transactions on Applied Mathematics
VL - 4
SP - 653
EP - 671
PY - 2023
DA - 2023/10
SN - 4
DO - http://doi.org/10.4208/csiam-am.SO-2022-0052
UR - https://global-sci.org/intro/article_detail/csiam-am/22073.html
KW - Sampling method, multi-frequency, sparse data, inverse source problems.
AB - <p style="text-align: justify;">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.</p>