Interpretable Modeling and Reduction of Unknown Errors in Mechanistic Operators

TL;DR

This paper introduces an interpretable neural approach to model and correct unknown errors in mechanistic forward operators, improving the accuracy of image reconstruction in medical imaging applications.

Contribution

It proposes a conditional generative model that embeds the mechanistic operator, enabling error correction and source identification within a traditional reconstruction framework.

Findings

Reduced errors in the forward operator in simulations

Improved accuracy of heart potential reconstruction in real data

Demonstrated interpretability of error sources

Abstract

Prior knowledge about the imaging physics provides a mechanistic forward operator that plays an important role in image reconstruction, although myriad sources of possible errors in the operator could negatively impact the reconstruction solutions. In this work, we propose to embed the traditional mechanistic forward operator inside a neural function, and focus on modeling and correcting its unknown errors in an interpretable manner. This is achieved by a conditional generative model that transforms a given mechanistic operator with unknown errors, arising from a latent space of self-organizing clusters of potential sources of error generation. Once learned, the generative model can be used in place of a fixed forward operator in any traditional optimization-based reconstruction process where, together with the inverse solution, the error in prior mechanistic forward operator can be minimized and the potential source of error uncovered. We apply the presented method to the reconstruction of heart electrical potential from body surface potential. In controlled simulation experiments and in-vivo real data experiments, we demonstrate that the presented method allowed reduction of errors in the physics-based forward operator and thereby delivered inverse reconstruction of heart-surface potential with increased accuracy.