Sparse reconstructions of acoustic source for inverse scattering problems in measure space
Sparse reconstructions of acoustic source for inverse scattering problems in measure space
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DOI：
10.1088/1361-6420/ab28cb
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发表时间：
2018-10
期刊：
影响因子：
2.1
通讯作者：
Xueshuang Xiang;Hongpeng Sun
中科院分区：
文献类型：
--
作者：
Xueshuang Xiang;Hongpeng Sun
本文对氡测量空间中给定声源的正散射和逆散射问题进行了系统的数学分析。对于直接问题，我们通过引入弱解的一个特殊定义，即非常弱解，研究了该问题的适定性，包括存在性、唯一性和稳定性。对于反问题，我们选择Radon测度空间而不是流行的L1空间来构建稀疏重构，可以保证重构解的存在性。利用对偶空间中的半光滑牛顿法可以解决稀疏重建问题。给出了数值算例。
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 L1 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.