Simultaneous Reconstruction and Uncertainty Quantification for Tomography

TL;DR

This paper introduces a Gaussian process-based method for simultaneous tomographic reconstruction and uncertainty quantification, effectively handling noisy and limited data while providing reliable confidence measures.

Contribution

It presents a novel approach that combines reconstruction with explicit uncertainty quantification using Gaussian processes, improving upon existing methods by incorporating prior knowledge and noise models.

Findings

Comparable reconstruction quality to existing methods

Effective quantification of solution uncertainties

Demonstrated robustness under various noise conditions

Abstract

Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of ground truth, quantifying the solution quality is highly desirable but under-explored. In this work, we address this challenge through Gaussian process modeling to flexibly and explicitly incorporate prior knowledge of sample features and experimental noises through the choices of the kernels and noise models. Our proposed method yields not only comparable reconstruction to existing practical reconstruction methods (e.g., regularized iterative solver for inverse problem) but also an efficient way of quantifying solution uncertainties. We demonstrate the capabilities of the proposed approach on various images and show its unique capability of uncertainty quantification in the presence of various noises.