Stochastic Convolutional Sparse Coding

TL;DR

This paper introduces a stochastic spatial-domain solver for convolutional sparse coding that outperforms traditional Fourier-domain methods in speed while maintaining quality, especially on large-scale datasets.

Contribution

A novel stochastic spatial-domain solver with randomized subsampling for convolutional sparse coding, extending to online learning for large datasets.

Findings

Outperforms Fourier-domain solvers in execution time

Maintains learning quality with appropriate subsampling rates

Learned dictionaries improve sparse representation of natural images

Abstract

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.