Abstract: Aiming at the problem of lacking of interpretability of deep image denoising networks,this paper proposes a multi-scale convolutional sparse coding network(MSCSC-Net)for image denoising using the idea of deep unfolding.Firstly,a multi-scale convolutional sparse coding(MSCSC)model is developed by exploiting the multi-scale convolutional dictionary,which can effectively express the multi-scale structure of image.Then,the traditional iterative optimization solution for solving the MSCSC model is unfolded into a deep neural network,namely MSCSC-Net.Each layer of MSCSC-Net corresponds to each iteration of the optimization solution.Therefore,the parameters of MSCSC-Net can be accurately defined through the traditional optimization model,which improves the interpretability.In addition,in order to preserve the structural of original image,the proposed MSCSC-Net adopts a revised residual learning idea,in which the weighted results of input noisy image and intermediate denoised image of previous layer are used as the input of next layer.Such revised residual learning can improve denoising performance further.Experimental results on public datasets show that MSCSC-Net is competitive to existing typical deep learning-based algorithms.Speci-fically,for the CBSD68 dataset at noise level 75,MSCSC-Net obtains 0.77% and 2.2% improvements over FFDNet in terms of the average PSNR and SSIM,respectively.

Key words: Image denoising, Multi-scale convolutional sparse coding, Residual learning, Deep neural network, Deep unfolding