  While convolutional sparse representations enjoy a number of useful
properties, they have received limited attention for image reconstruction
problems. The present paper compares the performance of block-based and
convolutional sparse representations in the removal of Gaussian white noise.
While the usual formulation of the convolutional sparse coding problem is
slightly inferior to the block-based representations in this problem, the
performance of the convolutional form can be boosted beyond that of the
block-based form by the inclusion of suitable penalties on the gradients of the
coefficient maps.
