Bayesian approach for limited-aperture inverse acoustic scattering with total variation prior

TL;DR

This paper introduces a Bayesian method with a total variation prior for reconstructing obstacle shapes in acoustic scattering from limited data, demonstrating promising numerical results.

Contribution

It presents a novel Bayesian framework with a total variation prior applied to Fourier coefficients for shape reconstruction in limited-aperture inverse scattering.

Findings

Effective shape reconstruction from limited data

Robustness of the total variation prior

Promising numerical performance

Abstract

In this work, we apply the Bayesian approach for the acoustic scattering problem to reconstruct the shape of a sound-soft obstacle using the limited-aperture far-field measure data. A novel total variation prior is assigned to the shape parameterization form. This prior is imposed on the Fourier coefficients of the parameterized form of the obstacle. Extensive numerical tests are provided to illustrate the numerical performance.