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

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 scheme is developed for the obstacle shape parameterization. It is imposed on the Fourier coefficients of the parameterization not the parameterization itself. Using this prior, some less smooth objects can be reconstructed. We also investigate the well-posedness in the sense of the Hellinger distance, Wasserstein distance and Kullback–Leibler divergence. Extensive numerical tests are provided to illustrate the numerical performance.

Keywords:

• Inverse acoustic scattering
• uncertainty quantification
• $l_1$ priors
• total variation prior

MSC 2020:

• 78A46
• 62F15
• 65N21

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Central Government Funds of Guiding Local Scientific and Technological Development for Sichuan Province No. 2021ZYD0007, NSFC No. 11601067.