Regularization is one of the most fundamental topics in optimization, statistics and machine learning.

Deep neural networks provide excellent performance for inverse problems such as denoising. However, neural networks can be sensitive to adversarial or worst-case perturbations. This raises the question of whether such networks can be trained efficiently to be worst-case robust.

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By now Bayesian methods are routinely used in practice for solving inverse problems.

Plug-and-Play (PnP) methods are efficient iterative algorithms for solving ill-posed image inverse problems. PnP methods are obtained by using deep Gaussian denois-ers instead of the proximal operator or the gradient-descent step within proximal algorithms.