No abstract

Deep image priors (DIP) offer a novel approach for the regularization that leverages the inductive bias of a deep convolutional architecture in inverse problems. However, the quality of DIP approaches often degrades when the number of iterations exceeds a certain threshold due to overfitting. To mitigate this effect, this work incorporates a plug-andplay prior scheme which can accommodate additional regularization steps within a DIP framework. Our modification is achieved using an augmented Lagrangian formulation of the problem, and is solved using an Alternating Direction Method of Multipliers (ADMM) variant, which can capture existing DIP approaches as a special case. We show experimentally that our ADMM-based DIP pairing outperforms competitive baselines in PSNR while exhibiting less overfitting.

We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of stochastic proximal-gradient-type methods for regularized empirical risk minimization. Second, when the activation functions is differentiable, it provides an upper bound on the Lipschitz constant of the network. Such bound is tighter than the trivial layer-wise product of Lipschitz constants, motivating its use for training networks robust to adversarial perturbations. In practical experiments we illustrate the advantages of using the proximal mapping and we compare the robustness-accuracy trade-off induced by the 1path-norm, L1-norm and layer-wise constraints on the Lipschitz constant (Parseval networks).