Given a source and a target probability measure, the Monge problem studies efficient ways to map the former onto the latter. This efficiency is quantified by defining a cost function between source and target data.

Logistic regression is commonly used for modeling dichotomous outcomes.

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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.

While this could be done using thesynthesis formulation, we demonstrate that this leads to slower performances. The main difficulty inapplying suchmethods intheanalysisformulation liesinproposing a way to compute the derivatives through the proximal operator.

In this paper we propose to use an old and surprisingly simple method due to Jacobi to compute these eigenvalue and singular value decompositions, and we demonstrate that it can lead to substantial gains in terms of computation time compared to standard approaches.