A Local Block Coordinate Descent Algorithm for the CSC Model

The Convolutional Sparse Coding (CSC) model has recently gained considerable traction in the signal and image processing communities. By providing a global, yet tractable, model that operates on the whole image, the CSC was shown to overcome several limitations of the patch-based sparse model while achieving superior performance in various applications. Contemporary methods for pursuit and learning the CSC dictionary often rely on the Alternating Direction Method of Multipliers (ADMM) in the Fourier domain for the computational convenience of convolutions, while ignoring the local characterizations of the image. In this work we propose a new and simple approach that adopts a localized strategy, based on the Block Coordinate Descent algorithm. The proposed method, termed Local Block Coordinate Descent (LoBCoD), operates locally on image patches. Furthermore, we introduce a novel stochastic gradient descent version of LoBCoD for training the convolutional filters. This Stochastic-LoBCoD leverages the benefits of online learning, while being applicable even to a single training image. We demonstrate the advantages of the proposed algorithms for image inpainting and multi-focus image fusion, achieving state-of-the-art results.