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We consider the problem of denoising with the help of prior information takenfrom a database of clean signals or images. Denoising with variational methodsis very efficient if a regularizer well adapted to the nature of the data isavailable. Thanks to the maximum a posteriori Bayesian framework, suchregularizer can be systematically linked with the distribution of the data.With deep neural networks (DNN), complex distributions can be recovered from alarge training database.To reduce the computational burden of this task, weadapt the compressive learning framework to the learning of regularizersparametrized by DNN. We propose two variants of stochastic gradient descent(SGD) for the recovery of deep regularization parameters from a heavilycompressed database. These algorithms outperform the initially proposed methodthat was limited to low-dimensional signals, each iteration using informationfrom the whole database. They also benefit from classical SGD convergenceguarantees. Thanks to these improvements we show that this method can beapplied for patch based image denoising.}

Batch-less stochastic gradient descent for compressive learning of deep regularization for image denoising