Fast Convolutional Sparse Coding

Abstract

Sparse coding has become an increasingly popular method in learning and vision for a variety of classification, reconstruction and coding tasks. The canonical approach intrinsically assumes independence between observations during learning. For many natural signals however, sparse coding is applied to sub-elements ( i.e. patches) of the signal, where such an assumption is invalid. Convolutional sparse coding explicitly models local interactions through the convolution operator, however the resulting optimization problem is considerably more complex than traditional sparse coding. In this paper, we draw upon ideas from signal processing and Augmented Lagrange Methods (ALMs) to produce a fast algorithm with globally optimal subproblems and super-linear convergence.