A New Sparse Recovery Method for the Inverse Acoustic Scattering Problem  

作　　者：Chang-long WANG Jun-xiong JIA Ji-gen PENG Shou-jin LIN 

机构地区：[1]Ministry Key Laboratory of Electronic Information Countermeasure and Simulation,Xidian University,Xi'an 710049,China [2]School of Mathematics and Statistics,Xi’an Jiaotong University,Xi’an 710049,China [3]School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China [4]LMTOR Intellignet Equipment Co.,Ltd,No.5 Fengsheng Road,Zhongshan,China

出　　处：《Acta Mathematicae Applicatae Sinica》2020年第1期49-66,共18页应用数学学报（英文版）

基　　金：partially supported by the NSFC(Nos.11771347,11871392);partially supported by the Major projects of the NSFC(Nos.91730306,41390450,41390454);partially supported by the National Science and Technology Major project(Nos.2016ZX05024-001-007 and 2017ZX050609)。

摘　　要：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.

关 键 词：SPARSE RECOVERY acoustic SCATTERER l0-minimization SUBSTITUTE function 

分 类 号：O42[理学—声学]