A Variational neural network for image restoration based on coupled regularizers

Variational neural networks based on unrolled optimization algorithms for image restoration have received considerable attentions recently because they inherit the merits of variational methods and deep learning methods in explanation and efficiency. Inspired by coupled regularizers adopted by variational models in vectorial image processing, we propose a novel variational neural network for image restoration making use of algorithm unfolding from isotropic and anisotropic coupled regularizers. The iterative schemes of variational models with coupled regularizers are designed using the proximal gradient descent method, which have exact correspondences with layers of deep neural networks. The diffusion operators are designed as convex combination of DCT(Discrete Cosine Transformation) bases with trainable parameters. The influence functions are designed via combination of Gauss radial basis functions, but they are shared by different channels of the same layer to ensure the simultaneous diffusion of all the channels during training, thanks to the coupled properties of regularizers. Compared with the classic TNRD(Trainable Networks for Reaction-Diffusion) model, the coupled isotropic diffusion terms can reduce training parameters greatly, and the coupled anisotropic diffusion terms have better adaptive properties in texture and edge preserving, which are demonstrated in extensive experiments on image denoising and super-resolution. The proposed variational neural networks via coupled regularizers can be easily extended to other image restoration tasks, such as image deblurring and demosaicking. The similar networks can be designed based on other iterative optimization algorithms, such as HQS and ADMM also.