While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep learning approaches is that they require an expensive retraining whenever the specific problem, the noise level, noise type, or desired measure of fidelity changes. On the contrary, variational methods have a plug-and-play nature as they usually consist of separate data fidelity and regularization terms. In this paper we study the possibility of replacing the proximal operator of the regularization used in many convex energy minimization algorithms by a denoising neural network. The latter therefore serves as an implicit natural image prior, while the data term can still be chosen arbitrarily. Using a fixed denoising neural network in exemplary problems of image deconvolution with different blur kernels and image demosaicking, we obtain state-of-the-art results. Additionally, we discuss novel results on the analysis of possible convex optimization algorithms to incorporate the network into, as well as the choices of algorithm parameters and their relation to the noise level the neural network is trained on.

本文研究探讨通过使用去噪神经网络替代凸优化算法中的正则化程式近算，使得数据项和正则化项可以独立选择并结合。在图像去模糊和去马赛克问题中，通过使用固定的去噪神经网络，本文取得了最先进的重建效果，并且该方法具有很高的通用性和较少的问题特定训练需求。

学习邻近算子：使用降噪网络来规则化逆成像问题