@Article{CSIAM-AM-4-653,
author = {Liu , Xiaodong and Meng , Shixu},
title = {A Multi-Frequency Sampling Method for the Inverse Source Problems with Sparse Measurements},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2023},
volume = {4},
number = {4},
pages = {653--671},
abstract = {<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>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2022-0052},
url = {http://global-sci.org/intro/article_detail/csiam-am/22073.html}
}