Learned Priors

Priors learned from example conductivities: denoisers used as proximal operators, learned energies, implicit networks, and what can go wrong.

Reading order.

1. Overview: Deep Learning for EIT, Learned Regularization, Manifold Hypothesis.
2. Denoisers as priors: Plug-and-Play Priors, Regularization by Denoising, with the U-Net as the typical architecture.
3. Learned energies: Energy-Based Models, Input Convex Neural Networks, Langevin Dynamics.
4. Implicit and continuous networks: Deep Equilibrium Models, Neural ODEs.
5. Risks: Hallucinations and Uncertainty.

Related. Classical penalties: Regularization; the connection: Classical and Learned Priors. Generative priors: Diffusion Models; symmetric architectures: Geometric Learning.

References

1. S. Arridge, P. Maass, O. Öktem, C.-B. Schönlieb (2019). Solving inverse problems using data-driven models. Acta Numer. 28, 1–174. doi:10.1017/S0962492919000059