Numerical comparison of iterative and functional-analytical algorithms for inverse acoustic scattering

TL;DR

This paper compares iterative and functional-analytical algorithms for inverse acoustic scattering, demonstrating their effectiveness and advantages in reconstructing different scatterer strengths through numerical experiments.

Contribution

It provides the first comparative numerical analysis of these algorithms for the 2D Helmholtz equation in acoustic tomography.

Findings

Iterative algorithm effectively reconstructs middle strength scatterers.

Functional-analytical approach excels in recovering strong scatterers.

Filtering in wave vector space improves iterative algorithm convergence.

Abstract

In this work the numerical solution of acoustic tomography problem based on the iterative and functional-analytical algorithms is considered. The mathematical properties of these algorithms were previously described in works of R.G.Novikov for the case of the Schr\"odinger equation. In the present work, for the case of two-dimensional scalar Helmholtz equation, the efficiency of the iterative algorithm in reconstruction of middle strength scatterers and advantages of the functional-analytical approach in recovering strong scatterers are demonstrated. A filtering procedure is considered in the space of wave vectors, which additionally increases the convergence of the iterative algorithm. Reconstruction results of sound speed perturbations demonstrate the comparable noise immunity and resolution of the considered algorithms when reconstructing middle strength scatterers. A comparative numerical investigation of the iterative and functional-analytical algorithms in inverse acoustic scattering problems is implemented in this work for the first time.