Modified forward and inverse Born series for the Calderon and diffuse-wave problems. (7th October 2020)

• Record Type: Journal Article
• Authors: Abhishek, Anuj; Bonnet, Marc; Moskow, Shari
• Is Part Of: Inverse problems. Volume 36:Number 11(2020)
• Publication Date: 2020-10-07
• Subjects: Calderon problem -- diffuse wave -- Born series; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abae11
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We propose a new direct reconstruction method based on series inversion for electrical impedance tomography (EIT) and the inverse scattering problem for diffuse waves. The standard Born series for the forward problem has the limitation that the series requires that the contrast lies within a certain radius for convergence. Here, we instead propose a modified Born series which converges for the forward problem unconditionally. We then invert this modified Born series and compare reconstructions with the usual inverse Born series. We also show that the modified inverse Born series has a larger radius of convergence.