Efficient Algorithm for Convolutional Dictionary Learning via Accelerated Proximal Gradient Consensus

Convolutional sparse representations are receiving an increase attention as a better alternative to the standard patch-based formulation for multiple image processing tasks. Several different algorithms based on ADMM, ADMM consensus and APG (Accelerated Proximal Gradient) have been proposed to efficiently solve the convolutional dictionary learning problem. Among them, ADMM consensus is considered as one of the fastest methods implemented in parallel due to its separable structure. However, its usage on large sets of images is computationally restricted by the dictionary update stage. In the present work, we propose a novel method to address this stage based on an APG consensus approach. This method considers particular strategies of the ADMM consensus and APG frameworks to develop a less complex solution decoupled across the training images. We show in our experimental results that the proposed method is significantly faster than the state-of-the-art consensus method implemented in serial and parallel while maintaining comparable performance in terms of reconstruction and sparsity metrics in denoising and inpainting tasks.