文献详情
Sparse reconstructions of acoustic source for inverse scattering problems in measure space
文献类型：期刊
通讯作者：Sun, HP (reprint author), Renmin Univ China, Inst Math Sci, Beijing 100872, Peoples R China.
期刊名称：INVERSE PROBLEMS影响因子和分区
年：2020
卷：36
期：3
ISSN：0266-5611
关键词：inverse acoustic scattering; inverse source problem; sparse reconstruction; Radon measure space; semismooth Newton method
所属部门：数学科学研究院
摘要：This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence, the uniqueness, and the stability by introducing a special definition of the weak solution, i.e. very weak solution. For the inverse problem, we choose the Radon measure space instead of the popular L-1 space to build the sparse reconstruction, which can guarant ...More
This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence, the uniqueness, and the stability by introducing a special definition of the weak solution, i.e. very weak solution. For the inverse problem, we choose the Radon measure space instead of the popular L-1 space to build the sparse reconstruction, which can guarantee the existence of the reconstructed solution. The sparse reconstruction problem can be solved by the semismooth Newton method in the dual space. Numerical examples are included. ...Hide

DOI：10.1088/1361-6420/ab28cb
百度学术：Sparse reconstructions of acoustic source for inverse scattering problems in measure space
语言：外文
基金：NSF of ChinaNational Natural Science Foundation of China [11501559]; Fundamental Research Funds for the Central UniversitiesFundamental Research Funds for the Central Universities; Renmin University of China [15XNLF20]; Alexander von Humboldt FoundationAlexander von Humboldt Foundation
作者其他论文



On an inverse elastic wave imaging scheme for nearly incompressible materials.Li, Jingzhi, Liu, Hongyu, Sun, Hongpeng,.IMA JOURNAL OF APPLIED MATHEMATICS. 2019, 84(2), 229-257.
Analysis of Fully Preconditioned Alternating Direction Method of Multipliers with Relaxation in Hilbert Spaces.Sun, Hongpeng,.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. 2019, 183(1), 199-229.
A Proximal Point Analysis of the Preconditioned Alternating Direction Method of Multipliers.Bredies, Kristian;Sun, Hongpeng.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS.2017,173(3),878-907.