Verification of a variational source condition for acoustic inverse medium scattering problems. (17th June 2015)

• Record Type: Journal Article
• Authors: Hohage, Thorsten; Weidling, Frederic
• Is Part Of: Inverse problems. Volume 31:Number 7(2015:Jul.)
• Publication Date: 2015-06-17
• Subjects: inverse medium scattering -- convergence rates -- variational source condition -- stability estimate; 47J06 -- 35Q60 -- 35R30 -- 47A52; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/7/075006
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of (logarithmic) rates of convergence for Tikhonov regularization under Sobolev smoothness assumptions for the refractive index. This is achieved by combining two lines of research, conditional stability estimates via geometrical optics solutions and variational regularization theory.