刘晓东教授学术报告

发布时间:2017年11月21日 作者:唐颖   消息来源:业务办    阅读次数:[]

题目: From limited-aperture to full-aperture

报告人: 刘晓东教授 中国科学院数学与系统科学研究院

报告时间:2017年11月24号星期五下午15:00-16:00

报告地点:数理楼145报告厅

摘要:

Many numerical methods have been proposed in the last 30 years for inverse problems. While very successful in many cases, progress has lagged in other areas of applications which are forced to rely on limited-aperture measurements. In this talk, we introduce some techniques to retrieve the other data that cannot be measured directly. We consider the inverse acoustic scattering of time harmonic plane waves and take the scattering amplitude to be the measurements. Assume that the scattering amplitude can only be measured with observation directions restricted in $S^{n-1}_0$, which is compactly supported in the unit sphere. Based on the reciprocity relation of the scattering amplitude, we prove a special symmetric structure of the corresponding multi-static response matrix. Combining this, with the help of the Green's formula for the scattered field, we introduce an iterative scheme to retrieve approximate full-aperture scattering amplitude. As an application, using a recently proposed direct sampling method [1], we consider the fast and robust sampling methods with limited-aperture measurements. Some numerical simulations are conducted with noisy data, and the results will further verify the effectiveness and robustness of the proposed data retrieval method and of the sampling method for inverse acoustic scattering problems. All the works have been generalized to inverse elastic scattering problems [3].

References:

[1] X. Liu, A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency, Inverse Problems 33, (2017), 085011.

[2] X. Liu, From limited-aperture to full-aperture, arXiv:1708.03029, 2017

[3] X. Ji, X. Liu and Y. Xi, Direct sampling methods for inverse elastic scattering problems, arXiv:1711.00626, 2017.



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