On the inverse problem of vibro-acoustography

TL;DR

This paper formulates vibroacoustic imaging as an inverse problem, proving uniqueness of parameter recovery and developing reconstruction algorithms within a rigorous mathematical framework.

Contribution

It introduces a mathematical model for vibroacoustic imaging, proves uniqueness of the inverse problem, and develops Newton and gradient-based reconstruction methods.

Findings

Proved uniqueness of the nonlinearity parameter recovery.

Developed Newton and gradient-based reconstruction algorithms.

Established a mathematical framework for vibroacoustic inverse problems.

Abstract

The aim of this paper is to put the problem of vibroacoustic imaging into the mathematical framework of inverse problems (more precisely, coefficient identification in PDEs) and regularization. We present a model in frequency domain, prove uniqueness of recovery of the spatially varying nonlinearity parameter from measurements of the acoustic pressure at multiple frequencies, and derive Newton as well as gradient based reconstruction methods.