Convolutional Dictionary Learning: A Comparative Review and New Algorithms
This work addresses a gap in the field by providing a comprehensive comparison for researchers and practitioners in signal processing and machine learning, though it is incremental as it builds on existing methods.
The paper tackles the challenging problem of convolutional dictionary learning by conducting a thorough comparative review of existing methods and proposing new algorithms that outperform them in certain contexts, with performance comparisons revealing a wide range of differences and identifying the most effective approaches.
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.