Characterizing impacts of model uncertainties in quantitative photoacoustics

TL;DR

This paper investigates how uncertainties in model parameters affect the accuracy of image reconstructions in quantitative photoacoustic imaging, providing analytical bounds and computational methods for error quantification.

Contribution

It introduces a sensitivity analysis framework and polynomial chaos expansion method to quantify model uncertainty impacts in PAT image reconstruction.

Findings

Analytical bounds on reconstruction errors derived for simplified models

Computational procedure for error quantification developed and demonstrated

Numerical simulations illustrate the effectiveness of the proposed methods

Abstract

This work is concerned with uncertainty quantification problems for image reconstructions in quantitative photoacoustic imaging (PAT), a recent hybrid imaging modality that utilizes the photoacoustic effect to achieve high-resolution imaging of optical properties of tissue-like heterogeneous media. We quantify mathematically and computationally the impact of uncertainties in various model parameters of PAT on the accuracy of reconstructed optical properties. We derive, via sensitivity analysis, analytical bounds on error in image reconstructions in some simplified settings, and develop a computational procedure, based on the method of polynomial chaos expansion, for such error characterization in more general settings. Numerical simulations based on synthetic data are presented to illustrate the main ideas.