Efficient ADMM-based Algorithms for Convolutional Sparse Coding
This work addresses efficiency improvements for convolutional sparse coding, which is incremental to existing methods in signal processing and machine learning.
The paper tackled the convolutional least-squares fitting subproblem in convolutional sparse coding, improving the efficiency of state-of-the-art ADMM-based algorithms and extending the approach to dictionary learning and error-constrained coding.
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.