Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 17-CNA-019 Stability and Error Estimates of BV Solutions to the Abel Inverse Problem Linan ZhangDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213linanz@andrew.cmu.edu Hayden SchaefferDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213schaeffer@cmu.eduAbstract: 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 $BV$ solutions to the Abel inverse problem, deriving a priori estimates on the recovery. In particular, we provide $L^2$-stability bounds on $BV$ solutions to the Abel inverse problem. These bounds yield error estimates on images reconstructed from a proposed total variation regularized minimization problem.Get the paper in its entirety as  17-CNA-019.pdf