We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field representing the objects. To construct the prior distribution we use a topological sensitivity analysis. We demonstrate the approach on the Bayesian solution of 2D inverse problems in light and acoustic holography with synthetic data. Statistical information on objects such as their center location, diameter size, orientation, as well as material properties, are extracted by sampling the posterior distribution. Assuming the number of objects known, comparison of the results obtained by Markov Chain Monte Carlo (MCMC) sampling and by sampling a Gaussian distribution found by linearization about the maximum a posteriori estimate show reasonable agreement. The latter procedure has low computational cost, which makes it an interesting tool for uncertainty studies in 3D. However, MCMC sampling provides a more complete picture of the posterior distribution and yields multi-modal posterior distributions for problems with larger measurement noise. When the number of objects is unknown, we devise a stochastic model selection framework.
|Original language||English (US)|
|State||Published - Oct 3 2020|
Bibliographical noteKAUST Repository Item: Exported on 2021-02-16
Acknowledged KAUST grant number(s): OSR-2018-CARF-3666
Acknowledgements: A Carpio and S Iakunin acknowledge partial support from the FEDER/MICINN-AEI grant MTM2017-84446-C2-1-R. G Stadler acknowledges partial support from the US National Science Foundation Grant #1723211 and from KAUST under Award #OSR-2018-CARF-3666. A Carpio thanks RE Caflisch for hospitality during a sabbatical stay at the Courant Institute, NYU, and DG Grier for an introduction to acoustic holography.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.