title: Solution of the nonlinear inverse scattering problem by T-matrix completion. II. Simulations.
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 [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043317 (2016)10.1103/PhysRevE.94.043317] 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.
authors.affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
authors.forename: Howard W
authors.initials: HW
authors.lastname: Levinson
authors.affiliation: Aix-Marseille Université, CNRS, Centrale Marseille, Institut Fresnel UMR 7249, 13013 Marseille, France.
authors.forename: Vadim A
authors.initials: VA
authors.lastname: Markel