Monotonicity in inverse obstacle scattering on unbounded domains. (20th August 2020)

• Record Type: Journal Article
• Authors: Albicker, Annalena; Griesmaier, Roland
• Is Part Of: Inverse problems. Volume 36:Number 8(2020)
• Publication Date: 2020-08-20
• Subjects: inverse scattering -- Helmholtz equation -- monotonicity -- far field operator -- obstacles; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab98a3
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider an inverse obstacle scattering problem for the Helmholtz equation with obstacles that carry mixed Dirichlet and Neumann boundary conditions. We discuss far field operators that map superpositions of plane wave incident fields to far field patterns of scattered waves, and we derive monotonicity relations for the eigenvalues of suitable modifications of these operators. These monotonicity relations are then used to establish a novel characterization of the support of mixed obstacles in terms of the corresponding far field operators. We apply this characterization in reconstruction schemes for shape detection and object classification, and we present numerical results to illustrate our theoretical findings.