Matching Pursuit Based Convolutional Sparse Coding

Convolutional sparse coding using the l(0,infinity )norm has been described as "a problem that operates locally while thinking globally". In this paper, we present a matching pursuit based greedy algorithm specifically tailored to the l(0,infinity) norm. We also propose a corresponding dictionary learning algorithm, which trains a local dictionary on a set of global images. Our approach is based on the convolutional relationship between the local dictionary and the global image. It operates locally while taking into account the global nature of the images. We demonstrate the usage of our proposed strategy for the task of image inpainting.