We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scatterers. The theoretical justification of our novel sampling method is based on a rigorous asymptotic model, a modified Helmholtz--Kirchhoff identity, and our previous work on the linear sampling method for random sources. Our numerical implementation incorporates boundary elements, Singular Value Decomposition, Tikhonov regularization, and Morozov's discrepancy principle. We showcase the robustness and accuracy of our algorithms with a series of numerical experiments.
Off-Grid Point-Scatterer Localization from Sparse Limited-Aperture Data via Hankel Completion
Southern University of Science and Technology（南方科技大学）；Shenzhen International Center for Mathematics（深圳国际数学中心）；School of Mathematics and Statistics, Hubei Center for Applied Mathematics, and Hubei Key Laboratory of Computational Science, Wuhan University（武汉大学数学与统计学院、应用数学湖北省协同创新中心、计算科学湖北省重点实验室）；School of Artificial Intelligence, Hubei Center for Applied Mathematics, and Hubei Key Laboratory of Computational Science, Wuhan University（武汉大学人工智能学院、应用数学湖北省协同创新中心、计算科学湖北省重点实验室）
Constructing probing functions for direct sampling methods for inverse scattering problems with limited-aperture data: finite space framework and deep probing network
