Recovery of singularities from a backscattering Born approximation for a biharmonic operator in 3D. (8th March 2018)

• Record Type: Journal Article
• Authors: Tyni, Teemu
• Is Part Of: Inverse problems. Volume 34:Number 4(2018:Apr.)
• Publication Date: 2018-03-08
• Subjects: biharmonic operator -- inverse problem -- inverse scattering -- Born approximation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaaf7f
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider a backscattering Born approximation for a perturbed biharmonic operator in three space dimensions. Previous results on this approach for biharmonic operator use the fact that the coefficients are real-valued to obtain the reconstruction of singularities in the coefficients. In this text we drop the assumption about real-valued coefficients and also establish the recovery of singularities for complex coefficients. The proof uses mapping properties of the Radon transform.