In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several recent papers have shown how convolutional neural networks (CNNs) can be extended to learn with graph-based data. In this work, we study the setting where the data (or measurements) are ordered, longitudinal or temporal in nature and live on a Riemannian manifold -- this setting is common in a variety of problems in statistical machine learning, vision and medical imaging. We show how recurrent statistical recurrent network models can be defined in such spaces. We give an efficient algorithm and conduct a rigorous analysis of its statistical properties. We perform extensive numerical experiments demonstrating competitive performance with state of the art methods but with significantly less number of parameters. We also show applications to a statistical analysis task in brain imaging, a regime where deep neural network models have only been utilized in limited ways.

Severalworksextend thesetodynamic scenes captured with monocular video, with promising performance.

Taking an example of hyperspectral image reconstruction, the spectral SCI [Gehm et al., 2007] can fast capture and compress 3D hyperspectral signals as

The ability to sense and reconstruct 3D appearance and geometry is critical to applications in vision, graphics, and beyond.

Moreover, the proposed method delivers impressive robustness at an extremely low scanning grid (i.e., 8

Consequently, these methods can hardly be deployed on resource-limited mobile devices.

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