The inside–outside duality for inverse scattering problems with near field data. (3rd July 2015)

• Record Type: Journal Article
• Authors: Lechleiter, Armin; Peters, Stefan
• Is Part Of: Inverse problems. Volume 31:Number 8(2015:Aug.)
• Publication Date: 2015-07-03
• Subjects: inside–outside duality -- near field data -- inverse scattering; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/8/085004
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We derive an inside–outside duality for near field scattering data generated by time-harmonic scattering of acoustic point sources from a sound-soft scatterer. This duality in particular rigorously characterizes interior Dirichlet eigenvalues of the scattering object by near field operators for an interval of wave numbers. As a crucial new concept to prove this duality we exploit the numerical ranges of certain modifications of these near field operators. We also show that our theoretical results can be numerically used to approximate interior Dirichlet eigenvalues from multi-frequency near field measurements.