Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems
This approach reduces the need for problem-specific training in imaging, benefiting researchers and practitioners in computational photography and medical imaging, though it is incremental as it builds on existing variational methods.
The paper tackles the inflexibility of deep learning methods for inverse imaging problems by using a fixed denoising neural network as a proximal operator in variational optimization, achieving state-of-the-art results in image deconvolution and demosaicking without retraining for different blur kernels.
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 their requirement for 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 independently. 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 reconstruction results. These indicate the high generalizability of our approach and a reduction of the need for problem-specific training. Additionally, we discuss novel results on the analysis of possible 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.