SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 188-224, March 2024.
Abstract. This paper is concerned with the problem of inverse scattering of time-harmonic acoustic plane waves by a two-layered medium with a locally rough interface in two dimensions. A direct imaging method is proposed to reconstruct the locally rough interface from the phaseless total-field data measured on the upper half of the circle with a large radius at a fixed frequency or from the phased far-field data measured on the upper half of the unit circle at a fixed frequency. The presence of the locally rough interface poses challenges in the theoretical analysis of the imaging methods. To address these challenges, a technically involved asymptotic analysis is provided for the relevant oscillatory integrals involved in the imaging methods, based mainly on the techniques and results in our recent work [L. Li, J. Yang, B. Zhang, and H. Zhang, arXiv:2208.00456, 2022] on the uniform far-field asymptotics of the scattered field for acoustic scattering in a two-layered medium. Finally, extensive numerical experiments are conducted to demonstrate the feasibility and robustness of our imaging algorithms.

中文翻译：

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从无相全场数据或相控远场数据重建局部粗糙界面的直接成像方法

SIAM 影像科学杂志，第 17 卷，第 1 期，第 188-224 页，2024 年 3 月。
摘要。本文研究的是二维局部粗糙界面的两层介质对时谐声平面波的逆散射问题。提出了一种直接成像方法，根据固定频率下大半径圆上半部测得的无相全场数据或圆上半部测得的相控远场数据来重建局部粗糙界面。固定频率下的单位圆。局部粗糙界面的存在对成像方法的理论分析提出了挑战。为了应对这些挑战，主要基于我们最近工作中的技术和结果，为成像方法中涉及的相关振荡积分提供了技术上涉及的渐近分析[L. Li, J. Yang, B.Zhang, 和 H.Zhang, arXiv:2208.00456, 2022] 关于两层介质中声散射的散射场的均匀远场渐进性。最后，进行了大量的数值实验来证明我们的成像算法的可行性和鲁棒性。