# Interpretable Modeling and Reduction of Unknown Errors in Mechanistic Operators

arXiv: https://arxiv.org/abs/2211.01373 · HTML: https://mlsanity.com/paper/2211.01373/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 7 of 7)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [DeepPET: A deep encoder-decoder network for directly solving the PET reconstruction inverse problem](https://mlsanity.com/paper/1804.07851/) (2018)
- [MRI Image Reconstruction via Learning Optimization Using Neural ODEs](https://mlsanity.com/paper/2006.13825/) (2020)
- [Learned Proximal Networks for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2008.05024/) (2020)
- [Improving the Flexibility and Robustness of Model-Based Derivative-Free Optimization Solvers](https://mlsanity.com/paper/1804.00154/) (2018)
- [DC-WCNN: A deep cascade of wavelet based convolutional neural networks for MR Image Reconstruction](https://mlsanity.com/paper/2001.02397/) (2020)
- [Generative Modeling and Inverse Imaging of Cardiac Transmembrane Potential](https://mlsanity.com/paper/1905.04803/) (2019)

## Abstract (arXiv)

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.