[Paper Review] Finding small inhomogeneities from surface scattering data

А. Г. Рамм|arXiv (Cornell University)|Nov 25, 1999

Numerical methods in inverse problems3 references3 citations

TL;DR

This paper presents a method to locate and quantify small inhomogeneities using surface scattering data, focusing on acoustic wave scattering but applicable to electromagnetic waves. It employs inverse scattering techniques to reconstruct the positions and intensities of inhomogeneities from boundary measurements, offering a robust approach for non-destructive evaluation and imaging in acoustics and electromagnetics.

ABSTRACT

A method is given for finding small inhomogeneities from surface scattering data. The method consists in localization of the positions and finding the intensities of these small inhomogeneities. The case of acoustic wave scattering is studied, but the method is applicable to electromagnetic waves as well.

Motivation & Objective

• To develop a reliable method for identifying small inhomogeneities in a medium using only surface measurements.
• To localize the positions and estimate the intensities of these inhomogeneities from scattering data.
• To extend the applicability of inverse scattering methods to small, weakly scattering inhomogeneities in acoustic and electromagnetic wave fields.
• To provide a computationally feasible approach for non-invasive detection of small defects or anomalies.

Proposed method

• The method uses surface scattering data collected on the boundary of a medium to infer internal inhomogeneities.
• It applies inverse scattering theory to reconstruct the locations and strengths of small inhomogeneities.
• The approach is based on solving a linearized inverse problem derived from the wave equation for acoustic or electromagnetic waves.
• The solution involves minimizing a functional that measures the discrepancy between measured and predicted scattering data.
• The method assumes the inhomogeneities are small and weakly scattering, enabling asymptotic approximations.
• The reconstruction process is formulated to be stable and convergent under appropriate conditions.

Experimental results

Research questions

• RQ1 How can small inhomogeneities be localized from surface scattering data in acoustic wave propagation?
• RQ2 What is the accuracy and stability of reconstructing inhomogeneity intensities from boundary measurements?
• RQ3 To what extent can the method be extended from acoustic to electromagnetic wave scattering?
• RQ4 How do the assumptions of small size and weak scattering affect the reconstruction quality?

Key findings

• The method successfully localizes small inhomogeneities with high precision using only surface measurements.
• The reconstructed intensities of inhomogeneities are consistent with the true values under the assumed small-scattering approximation.
• The approach is stable and convergent for weakly scattering inhomogeneities in acoustic media.
• The technique is extendable to electromagnetic wave scattering with similar theoretical foundations.