Bayesian Formulation of Acousto-Electric Tomography and Quantified Uncertainty in Limited View

TL;DR

This paper develops a Bayesian approach for acousto-electric tomography, modeling conductivity as a random field, and demonstrates improved reconstruction and uncertainty quantification from limited view data.

Contribution

It introduces a Bayesian framework for AET inverse problems, compares L1 and L2 likelihoods, and analyzes uncertainty in conductivity reconstructions with limited boundary access.

Findings

Small inclusions near accessible boundary can be reconstructed from single measurements.

Bayesian methods provide quantification of reconstruction uncertainty.

Both L1 and L2 likelihoods are effective for different limited view scenarios.

Abstract

Acousto-electric tomography (AET) is a hybrid imaging modality that combines electrical impedance tomography with focused ultrasound perturbations to obtain interior power density measurements, which provide additional information that can enhance the stability of conductivity reconstruction. In this work, we study the AET inverse problem within a Bayesian framework and compare statistical reconstruction with analytical approaches. The unknown conductivity is modeled as a random field, and inference is based on the posterior distribution conditioned on the measurements. We consider likelihood constructions based on both L1- and L2-type data misfit norms and establish Bayesian well-posedness for both formulations within the framework of Stuart (2010). Numerical experiments investigate the performance of the Bayesian method from noisy power density measurements using the L1 and L2 likelihood functions and a smooth prior and a piecewise-constant prior for different limited view configurations, including severely limited boundary access. In particular, we demonstrate that small inclusions near the accessible boundary can be reconstructed from AET data corresponding to a single EIT measurement, and we quantify reconstruction uncertainty through posterior statistics.