Convolutional sparse representations as an image model for impulse noise restoration

Standard sparse representations, applied independently to a set of overlapping image blocks, are a very effective approach to a wide variety of image reconstruction problems. Convolutional sparse representations, which provide a single-valued representation optimised over an entire image, provide an alternative form of sparse representation that has recently started to attract interest for image reconstruction problems. The present paper provides some insight into the suitability of the convolutional form for this type of application by comparing its performance as an image model with that of the standard model in an impulse noise restoration problem.