Fast Convolutional Sparse Coding ( FCSC )

Convolutional sparse coding remedies the shortcomings of the traditional (patch-based) sparse coding by modeling shift invariance directly. This yields more parsimonious coding schemes but increases complexity by coupling the coding problem for neighboring image patches where they overlap. Here we describe an optimization approach which exploits the separability of convolution across bands in the frequency domain in order to make dictionary learning efficient. Our presentation follows the notation in the paper of [Bristow et al. IEEE CVPR 2013] but includes additional implementation details and corrects some inaccuracies and typos. 1