Separable Dictionary Learning for Convolutional Sparse Coding via Split Updates

Existing methods for constructing separable 2D dictionary filter banks approximate a set of $K$ non-separable filters via a linear combination of $R\ll K$ separable filters. This approach involves the inefficiency of learning an initial set of non-separable filters, and places an upper bound on the quality of the separable filter banks. In this paper, we propose a method to directly learn a set of $K$ separable dictionary filters from a given image training set by drawing ideas from convolutional dictionary learning (CDL) methods. We show that the separable filters obtained by our method match the performance of an equivalent number of non-separable filters. Furthermore, the computational performance of our learning method is shown to be substantially faster than a state-of-the-art non-separable CDL method for large numbers of filters or large training sets.