2021/09/03 by Xiaodong Liu, Liu, Xiaodong, Shixu Meng +1
Engineering · Mathematics · #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.2109.01434
openalex publication_date 2021/09/03 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28
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.