Iterative reconstruction of the wavespeed for the wave equation with bounded frequency boundary data

TL;DR

This paper investigates an inverse boundary value problem for the wave equation with bounded frequency data, establishing conditions for iterative methods to reconstruct wavespeed functions effectively.

Contribution

It introduces classes of nonsmooth coefficient functions ensuring the applicability of steepest descent and Newton methods for inverse wave problems.

Findings

Identifies conditions for the data and coefficients for iterative methods to converge.

Provides a framework for applying optimization techniques to inverse wave problems.

Enhances understanding of wave speed reconstruction with bounded frequency data.

Abstract

We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth coefficient functions so that optimization formulations of inverse wave problems satisfy the prerequisites for application of steepest descent and Newton-type iterative methods.