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A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency
Liu, Xiaodong
2017-08-01
Source PublicationINVERSE PROBLEMS
ISSN0266-5611
Volume33Issue:8Pages:20
AbstractA sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very easy and simple to implement. With the help of the factorization of the far field operator, we establish an inf-criterion for characterization of underlying scatterers. This result is then used to give a lower bound of the proposed indicator functional for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functional decays like the bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functional continuously depends on the scattering amplitude, this further implies that the novel sampling method is extremely stable with respect to errors in the data. Different to the classical sampling method such as the linear sampling method or the factorization method, from the numerical point of view, the novel indicator takes its maximum near the boundary of the underlying target and decays like the bessel functions as the sampling points go away from the boundary. The numerical simulations also show that the proposed sampling method can deal with multiple multiscale case, even the different components are close to each other.
Keywordacoustic scattering scattering amplitude bessel functions multiple multiscale
DOI10.1088/1361-6420/aa777d
Language英语
Funding ProjectNNSF of China[11571355] ; NNSF of China[61379093] ; NNSF of China[91430102]
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Mathematical
WOS IDWOS:000406522600004
PublisherIOP PUBLISHING LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/441
Collection应用数学研究所
Corresponding AuthorLiu, Xiaodong
AffiliationChinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Liu, Xiaodong. A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency[J]. INVERSE PROBLEMS,2017,33(8):20.
APA Liu, Xiaodong.(2017).A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency.INVERSE PROBLEMS,33(8),20.
MLA Liu, Xiaodong."A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency".INVERSE PROBLEMS 33.8(2017):20.
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