3 papers
math.OC2025
Notes on the discretization of TV-norm regularized inverse potential problems
L Baratchart, D P Hardin, C Villalobos-Guillén
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, comp…
math.FA2020
Divergence-free measures in the plane and inverse potential problems in divergence form
L. Baratchart, D. Hardin, C. Villalobos-Guillén
We show that a divergence-free measure on the plane is a continuous sum of unit tangent vector fields on rectifiable Jordan curves. This loop decomposition is more precise than the…
math.OC2018
Inverse Potential Problems for Divergence of Measures with Total Variation Regularization
Laurent Baratchart, Cristobal Villalobos Guillen, Douglas P. Hardin +2
We study inverse problems for the Poisson equation with source term the divergence of an -valued measure, that is, the potential satisfies $$ ΔΦ= \text{div} \bold…