Efficient ADMM-based Algorithms for Convolutional Sparse Coding

TL;DR

This paper introduces an efficient ADMM-based approach for convolutional sparse coding and dictionary learning, significantly improving computational performance and enabling error-constrained sparse coding.

Contribution

It presents a novel solution to the convolutional least-squares subproblem, enhancing the efficiency of existing algorithms and extending them to error-constrained scenarios.

Findings

Improved efficiency of convolutional sparse coding algorithms

Development of a fast convolutional dictionary learning method

Introduction of an error-constrained convolutional sparse coding algorithm

Abstract

Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers and the convolution theorem. The only major difference between these methods is how they approach a convolutional least-squares fitting subproblem. This letter presents a solution to this subproblem, which improves the efficiency of the state-of-the-art algorithms. We also use the same approach for developing an efficient convolutional dictionary learning method. Furthermore, we propose a novel algorithm for convolutional sparse coding with a constraint on the approximation error.