Inverse wave-number-dependent source problems for the Helmholtz equation
Abstract
This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some time-dependent source with a priori given radiating period. Using the multi-frequency far-field data at a fixed observation direction, we provide a computational criterion for characterizing the smallest strip containing the support and perpendicular to the observation direction. The far-field data from sparse observation directions can be used to recover a -convex polygon of the support. The inversion algorithm is proven valid even with multi-frequency near-field data in three dimensions. The connections to time-dependent inverse source problems are discussed in the near-field case. Numerical tests in both two and three dimensions are implemented to show effectiveness and feasibility of the approach. This paper provides numerical analysis for a frequency-domain approach to recover the support of an admissible class of time-dependent sources.
Cite
@article{arxiv.2305.07459,
title = {Inverse wave-number-dependent source problems for the Helmholtz equation},
author = {Hongxia Guo and Guanghui Hu},
journal= {arXiv preprint arXiv:2305.07459},
year = {2024}
}