A Linearized Boundary Control Method for the Acoustic Inverse Boundary Value Problem

TL;DR

This paper introduces a linearized boundary control method for the acoustic inverse boundary value problem, providing a stable reconstruction formula for potential identification from boundary measurements, validated through numerical experiments.

Contribution

It develops a novel linearized boundary control approach with stability analysis and practical implementation for acoustic inverse problems.

Findings

Lipschitz stability at zero potential linearization

Hölder stability at nonzero potential linearization

Numerical validation of the reconstruction formula

Abstract

We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a reconstruction formula based on the boundary control method and prove that it is of Lipschitz-type stability. When the linearization is at a nonzero potential, we prove that the problem is of H\"{o}lder-type stability. The proposed reconstruction formula is implemented and evaluated using several numerical experiments to validate its feasibility.