  Convolutional sparse representations are a form of sparse representation with
a dictionary that has a structure that is equivalent to convolution with a set
of linear filters. While effective algorithms have recently been developed for
the convolutional sparse coding problem, the corresponding dictionary learning
problem is substantially more challenging. Furthermore, although a number of
different approaches have been proposed, the absence of thorough comparisons
between them makes it difficult to determine which of them represents the
current state of the art. The present work both addresses this deficiency and
proposes some new approaches that outperform existing ones in certain contexts.
A thorough set of performance comparisons indicates a very wide range of
performance differences among the existing and proposed methods, and clearly
identifies those that are the most effective.
