Support identification for parameter variations in a PDE system via regularized methods

TL;DR

This paper introduces a hybrid regularization method combining monotonicity principles and TSVD to accurately identify the support of parameter variations in PDE systems from boundary data, with demonstrated robustness and practical effectiveness.

Contribution

It develops a novel combined regularization approach for stable support identification in PDE inverse problems, improving accuracy especially for disjoint supports.

Findings

Enhanced support localization with hybrid regularization

Robustness against measurement noise demonstrated

Numerical experiments confirm practical applicability

Abstract

We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity properties of the Neumann-to-Dirichlet operator, which provides a theoretical foundation for stable support identification. To improve reconstruction accuracy, particularly when parameters have disjoint supports, we propose a combined regularization approach integrating monotonicity principles with Truncated Singular Value Decomposition (TSVD) regularization. This hybrid strategy enhances robustness against noise and ensures sharper support localization. Numerical experiments demonstrate the effectiveness of the proposed method, confirming its applicability in practical scenarios with varying parameter configurations.