Interpretable Modeling and Reduction of Unknown Errors in Mechanistic Operators
This work addresses errors in physics-based models for medical imaging reconstruction, offering an interpretable correction method that is incremental in improving existing optimization-based approaches.
The authors tackled the problem of unknown errors in mechanistic forward operators for image reconstruction by embedding the operator within a neural function and using a conditional generative model to correct errors interpretably, resulting in increased accuracy in heart-surface potential reconstruction in simulation and real data experiments.
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.