Notes on the discretization of TV-norm regularized inverse potential problems
L Baratchart (FACTAS), D P Hardin, C Villalobos-Guill\'en
TL;DR
This paper presents a discretization method for TV-norm regularized inverse potential problems involving linear inverse problems with measures, focusing on a quadratic residual criterion and total variation penalization.
Contribution
It introduces a novel discretization approach for inverse problems with measures and TV regularization, applicable to 3-D measure spaces.
Findings
Effective discretization of inverse problems with TV regularization
Applicable to 3-D measures with compact support
Potential for improved numerical solutions
Abstract
We describe a method to discretize optimization problems arising in the regularization of linear inverse problem having compact forward operator defined on 3-D valed measures, compactly supported on a fixed set. The criterion is a quadratic residual attached to the data, with an additive penalization of the total variation of the measure.
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Taxonomy
TopicsNumerical methods in inverse problems · Statistical and numerical algorithms · Sparse and Compressive Sensing Techniques