Label-Free Physics-Informed Image Sequence Reconstruction with Disentangled Spatial-Temporal Modeling

Traditional approaches to image reconstruction uses physicsbased loss with data-efficient inference, although the difficulty to properly model the inverse solution precludes learning the reconstruction across a distribution of data. Modern deep learning approaches enable expressive modeling but rely on a large number of reconstructed images (labeled data) that are often not available in practice. To combine the best of the above two lines of works, we present a novel label-free image reconstruction network that is supervised by physics-based forward operators rather than labeled data. We further present an expressive yet disentangled spatial-temporal modeling of the inverse solution, where its latent dynamics is modeled by neural ordinary differential equations and its emission over non-Euclidean geometrical domains by graph convolutional neural networks. We applied the presented method to reconstruct electrical activity on the heart surface from body-surface potential. In simulation and real-data experiments in comparison to both traditional physicsbased and modern data-driven reconstruction methods, we demonstrated the ability of the presented method to learn how to reconstruct using observational data without any corresponding labels.