2025/05/30 by Chun Liu, Liu, Chun, Guanghui Hu +5
Engineering · Mathematics · Medicine · #35P25 #35R30 #65N21 #Analysis of PDEs (math.AP) #FOS: Mathematics #Near-Field Optical Microscopy #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Ultrasound Imaging and Elastography
paper · pdf · doi:10.48550/arxiv.2505.24288
openalex publication_date 2025/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the location and shape of the obstacle from near-field data generated by infinitely many incident point source waves at a fixed energy. The incident point sources and the receivers for recording scattered signals are both located on a spherical closed surface, on which an outgoing-to-incoming operator is defined for facilitating the factorization of the near-field operator. Numerical examples in 2D are presented to show the validity and accuracy of the inversion algorithm.