A variational PDNet network using a learning reaction–diffusion equation

Due to their high performance in modeling and forecasting a large amount of real-world complex phenomena, deep convolutional neural networks have received a great deal of attention over the past ten years. It has been extensively utilized in several recent vision problems, such as image denoising and deblurring. By incorporating recent developments in learning-based nonlinear diffusion models and highlighting the connection between partial differential equations (PDEs) and networks, especially residual networks, we propose a flexible learning reaction–diffusion system with spatially computed convolution kernels. This trained PDE is employed to prevent the low-level features from deteriorating, which is needed for tasks involving denoising. In fact, we introduce an improved network architecture for a denoising network entitled VPDNet through an optimal control problem. More precisely, the network architecture is governed by an explicit Euler discretization of a reaction–diffusion system. We give the main algorithm to identify the kernel parameters using the Alternating Direction Method of Multipliers (ADMM) combined with a Primal-Dual algorithm. Finally, numerical simulations are provided with appropriate comparisons to demonstrate the efficiency of the elaborated network.