Designing and Learning Trainable Priors with Non-Cooperative Games

We introduce a general framework for designing and learning neural networks whose forward passes can be interpreted as solving convex optimization problems, and whose architectures are derived from an optimization algorithm. We focus on non-cooperative convex games, solved by local agents represented by the nodes of a graph and interacting through regularization functions. This approach is appealing for solving imaging problems, as it allows the use of classical image priors within deep models that are trainable end to end. The priors used in this presentation include variants of total variation, Laplacian regularization, sparse coding on learned dictionaries, and non-local self similarities. Our models are parameter efficient and fully interpretable, and our experiments demonstrate their effectiveness on a large diversity of tasks ranging from image denoising and compressed sensing for fMRI to dense stereo matching.