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

• Subject Area: Mathematics
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 258734477

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.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1173: Wave phenomena: analysis and numerics
• Applicant Institution: Karlsruher Institut für Technologie
• Project Heads: Privatdozent Dr. Tilo Arens; Professor Dr. Roland Griesmaier