Publication 17-CNA-019
Stability and Error Estimates of BV Solutions to the Abel Inverse Problem
Linan Zhang
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
linanz@andrew.cmu.edu
Hayden Schaeffer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
schaeffer@cmu.edu
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 $BV$ 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.
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