Convolutional Dictionary Learning: A Comparative Review and New Algorithms

TL;DR

This paper reviews convolutional dictionary learning algorithms, compares their performance comprehensively, and introduces new methods that outperform existing ones in specific scenarios.

Contribution

It provides a thorough comparison of existing algorithms and proposes new approaches that improve performance in convolutional dictionary learning.

Findings

Significant performance differences among existing methods

New algorithms outperform some existing methods in certain contexts

Clear identification of the most effective algorithms

Abstract

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.