A New Sparse Recovery Method for the Inverse Acoustic Scattering Problem

Based on sparse information recovery, we develop a new method for locating multiple multiscale acoustic scatterers. Firstly, with the prior information of the scatterers’ shape, we reformulate the location identification problem into a sparse information recovery model which brought the power of sparse recovery method into this type of inverse scattering problems. Specifically, the new model can advance the judgment of the existence of alternative scatterers and, in the meantime, conclude the number and locating of each existing scatterers. Secondly, as well known, the core model (l₀-minimization) in sparse information recovery is an NP-hard problem. According to the characteristics of the proposed sparse model, we present a new substitute method and give a detailed theoretical analysis of the new substitute model. Relying on the properties of the new model, we construct a basic algorithm and an improved one. Finally, we verify the validity of the proposed method through two numerical experiments.