Inverse potential problems for divergence of measures with total variation regularization (Q2216254)

This article discusses the inverse problem for the Poisson equation \(\Delta \Phi=\nabla \cdot \mu\), where \(\mu\) is an unknown signed Borel measure in \(\mathbb{R}^3\) to be recovered. The authors investigate methods for recovering \(\mu\) by penalizing the measure theoretic total variation norm. Sufficient conditions for the unique recovery of \(\mu\) are provided. Numerical examples are included to illustrate the main theoretical results.