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We introduce a general framework for designing and training neural networklayers whose forward passes can be interpreted as solving non-smooth convexoptimization problems, and whose architectures are derived from an optimizationalgorithm. We focus on convex games, solved by local agents represented by thenodes of a graph and interacting through regularization functions. Thisapproach is appealing for solving imaging problems, as it allows the use ofclassical image priors within deep models that are trainable end to end. Thepriors used in this presentation include variants of total variation, Laplacianregularization, bilateral filtering, sparse coding on learned dictionaries, andnon-local self similarities. Our models are fully interpretable as well asparameter and data efficient. Our experiments demonstrate their effectivenesson a large diversity of tasks ranging from image denoising and compressedsensing for fMRI to dense stereo matching.

A Flexible Framework for Designing Trainable Priors with Adaptive Smoothing and Game Encoding