We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is available. Thanks to the maximum a posteriori Bayesian framework, such regularizer can be systematically linked with the distribution of the data. With deep neural networks (DNN), complex distributions can be recovered from a large training database.To reduce the computational burden of this task, we adapt the compressive learning framework to the learning of regularizers parametrized by DNN. We propose two variants of stochastic gradient descent (SGD) for the recovery of deep regularization parameters from a heavily compressed database. These algorithms outperform the initially proposed method that was limited to low-dimensional signals, each iteration using information from the whole database. They also benefit from classical SGD convergence guarantees. Thanks to these improvements we show that this method can be applied for patch based image denoising.}

翻译：我们考虑利用来自干净信号或图像数据库的先验信息进行去噪的问题。如果存在一个与数据性质良好适配的正则化器，变分法去噪会非常高效。借助最大后验贝叶斯框架，这种正则化器可以与数据分布系统地关联起来。通过深度神经网络（DNN），可以从大型训练数据库中恢复复杂分布。为降低此任务的计算负担，我们将压缩学习框架适配到由DNN参数化的正则化器学习上。我们提出了两种随机梯度下降（SGD）变体，用于从高度压缩的数据库中恢复深度正则化参数。这些算法优于最初提出的局限于低维信号的方法（该方法每次迭代使用整个数据库的信息）。它们还享有经典SGD的收敛保证。借助这些改进，我们证明该方法可应用于基于块的图像去噪。