Efficient ADMM-based Algorithms for Convolutional Sparse 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. In this letter, we present a novel solution for this subproblem, which improves the computational efficiency of the existing algorithms. The same approach is also used to develop an efficient dictionary learning method. In addition, we propose a novel algorithm for convolutional sparse coding with a constraint on the approximation error. Source codes for the proposed algorithms are available online.