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.

本文介绍卷积稀疏表示作为一种稀疏表示的形式，其字典结构相当于一组线性滤波器的卷积。虽然最近已经开发出有效的算法来解决卷积稀疏编码问题，但相应的字典学习问题更加具有挑战性。此外，虽然已经提出了许多不同的方法，但缺乏彼此之间的彻底比较，使得很难确定哪个方法代表了当前的技术水平。本文既解决了这个缺陷，同时还提出了一些在某些环境下胜过现有方法的新方法。一组彻底的性能比较表明，现有和提出的方法之间存在着非常大的性能差异，并明确确定了最有效的方法。