Adaptive refinement and selection process through defect localization for reconstructing an inhomogeneous refraction index

TL;DR

This paper introduces an iterative method for reconstructing inhomogeneous acoustic refraction indices that uses defect localization to adaptively refine parameters, reducing complexity while maintaining accuracy.

Contribution

It presents two novel enhancements—parameter selection and adaptive refinement—based on defect localization to improve reconstruction efficiency and precision.

Findings

Parameter reduction without loss of accuracy

Effective adaptive refinement demonstrated numerically

Enhanced reconstruction with fewer parameters

Abstract

We consider the iterative reconstruction of both the internal geometry and the values of an inhomogeneous acoustic refraction index through a piecewise constant approximation. In this context, we propose two enhancements intended to reduce the number of parameters to reconstruct, while preserving accuracy. This is achieved through the use of geometrical informations obtained from a previously developed defect localization method. The first enhancement consists in a preliminary selection of relevant parameters, while the second one is an adaptive refinement to enhance precision with a low number of parameters. Each of them is numerically illustrated.