Image Denoising Using Convolutional Sparse Coding Network with Dry Friction

Convolutional sparse coding model has been successfully used in some tasks such as signal or image processing and classification. The recently proposed supervised convolutional sparse coding network (CSCNet) model based on the Minimum Mean Square Error (MMSE) approximation shows the similar PSNR value for image denoising problem with state of the art methods while using much fewer parameters. The CSCNet uses the learning convolutional iterative shrinkage-thresholding algorithms (LISTA) based on the convolutional dictionary setting. However, LISTA methods are known to converge to local minima. In this paper we proposed one novel algorithm based on LISTA with dry friction, named LISTDFA. The dry friction enters the LISTDFA algorithm through proximal mapping. Due to the nature of dry friction, the LISTDFA algorithm is proven to converge in a finite time. The corresponding iterative neural network preserves the computational simplicity of the original CSCNet, and can reach a better local minima practically.