Solution of the inverse scattering problem by T-matrix completion. II. Simulations

TL;DR

This paper demonstrates that the DCTMC method effectively solves nonlinear inverse scattering problems, accurately reconstructing object shape and contrast in ultrasound and seismic imaging through simulations.

Contribution

It extends the DCTMC approach to practical simulations, showing its capability to recover medium susceptibility in strongly nonlinear inverse scattering problems.

Findings

DCTMC successfully reconstructs object shape and contrast.

The method handles large data sets effectively.

Simulations validate DCTMC's applicability to ultrasound and seismic tomography.

Abstract

This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of scalar waves. The underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility. The simulations are relevant to ultrasound tomographic imaging and seismic tomography. It is shown that DCTMC is a viable method for solving strongly nonlinear inverse problems with large data sets. It provides not only the overall shape of the object but the quantitative contrast, which can correspond, for instance, to the variable speed of sound in the imaged medium.