Uncertainty principles for inverse source and inverse scattering problems (C06)

逆源和逆散射问题的不确定性原理（C06）

• 批准号: 427721392
• 金额: --
• 依托单位: Institut für Angewandte und Numerische Mathematik
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/427721392?language=en
• 关键词: Uncertainty; principles; inverse; source; scattering

Inverse source and inverse scattering problems are ill-posed inverse problems, where the goal is to recover information about sources or scatterers from remote observations of associated radiated or scattered waves. Structural information contained in the observed data can be used to establish uniqueness results, devise new types of reconstruction algorithms, and improve their stability. In this project, we study two particular types of such structural information: uncertainty principles and monotonicity relations. We will focus on (1) uncertainty principles, stability results, and reconstruction algorithms for source problems with broadband multifrequency observations, (2) combining far field splitting and phase retrieval, (3) a stable numerical implementation of monotonicity-based shape characterizations, and (4) monotonicity principles and monotonicity-based shape characterizations for time-dependent inverse scattering problems.

逆源和逆散射问题是不适定的逆问题，其目标是从相关辐射或散射波的远程观测中恢复关于源或散射体的信息。包含在观测数据中的结构信息可以用于建立唯一性结果，设计新类型的重建算法，并提高其稳定性。在这个项目中，我们研究了两种特殊类型的结构信息：不确定性原理和单调性关系。我们将重点关注（1）宽带多频观测源问题的不确定性原理，稳定性结果和重建算法，（2）结合远场分裂和相位恢复，（3）基于单调性的形状特征的稳定数值实现，以及（4）时间相关逆散射问题的单调性原理和基于单调性的形状特征。