Learning Geometry-Dependent and Physics-Based Inverse Image Reconstruction

TL;DR

This paper introduces a novel non-Euclidean neural network architecture that explicitly models geometry-dependent physics for inverse image reconstruction, demonstrating improved generalization across different geometries in biomedical applications.

Contribution

The paper presents a non-Euclidean encoding-decoding network that incorporates geometry-dependent physics via a bipartite graph, advancing inverse imaging in non-Euclidean spaces.

Findings

Enhanced generalization across geometrical variations

Superior performance over Euclidean models in biomedical reconstruction

Effective modeling of physics-dependent geometry in neural networks

Abstract

Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper, we present a new approach to learn inverse imaging that exploit the underlying geometry and physics. We first introduce a non-Euclidean encoding-decoding network that allows us to describe the unknown and measurement variables over their respective geometrical domains. We then learn the geometry-dependent physics in between the two domains by explicitly modeling it via a bipartite graph over the graphical embedding of the two geometry. We applied the presented network to reconstructing electrical activity on the heart surface from body-surface potential. In a series of generalization tasks with increasing difficulty, we demonstrated the improved ability of the presented network to generalize across geometrical changes underlying the data in comparison to its Euclidean alternatives.