  State-of-the-art methods for Convolutional Sparse Coding usually employ
Fourier-domain solvers in order to speed up the convolution operators. However,
this approach is not without shortcomings. For example, Fourier-domain
representations implicitly assume circular boundary conditions and make it hard
to fully exploit the sparsity of the problem as well as the small spatial
support of the filters. In this work, we propose a novel stochastic
spatial-domain solver, in which a randomized subsampling strategy is introduced
during the learning sparse codes. Afterwards, we extend the proposed strategy
in conjunction with online learning, scaling the CSC model up to very large
sample sizes. In both cases, we show experimentally that the proposed
subsampling strategy, with a reasonable selection of the subsampling rate,
outperforms the state-of-the-art frequency-domain solvers in terms of execution
time without losing the learning quality. Finally, we evaluate the
effectiveness of the over-complete dictionary learned from large-scale
datasets, which demonstrates an improved sparse representation of the natural
images on account of more abundant learned image features.
