CORNET: COMPOSITE-REGULARIZED NEURAL NETWORK FOR CONVOLUTIONAL SPARSE CODING

Sparse recovery via composite regularization is an interesting approach proposed recently in the literature. One could design non-convex regularizers through a convex combination of sparsity-promoting penalties with known proximal operators. We develop a new algorithm, namely, convolutional proximal-averaged thresholding algorithm (C-PATA) for {\it composite-regularized} convolutional sparse coding (CR-CSC) based on the recently proposed idea of proximal averaging. We develop an autoencoder structure based on the deep-unfolding of C-PATA iterations into neural network layers, which results in the composite-regularized neural network (CoRNet) architecture. The convolutional learned iterative soft-thresholding algorithm becomes a special case of CoRNet. We demonstrate the efficacy of CoRNet considering applications to image denoising and inpainting, and compare the performance with state-of-the-art techniques such as BM3D, convolutional LISTA, and fast and flexible convolutional sparse coding (FFCSC).