Stability and error estimates of BV solutions to the Abel inverse problem. (1st August 2018)

• Record Type: Journal Article
• Authors: Zhang, Linan; Schaeffer, Hayden
• Is Part Of: Inverse problems. Volume 34:Number 10(2018:Oct.)
• Publication Date: 2018-08-01
• Subjects: Abel transform -- total variation -- integral transforms -- ill-posed inverse problems -- stability; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aad1c7
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Reconstructing images from ill-posed inverse problems often utilizes total variation regularization in order to recover discontinuities in the data while also removing noise and other artifacts. Total variation regularization has been successful in recovering images for (noisy) Abel transformed data, where object boundaries and data support will lead to sharp edges in the reconstructed image. In this work, we analyze the behavior of solutions to the Abel inverse problem, deriving a priori estimates on the recovery. In particular, we provide L 2 -stability bounds on solutions to the Abel inverse problem. These bounds yield error estimates on images reconstructed from a proposed total variation regularized minimization problem.