# Scalable Online Convolutional Sparse Coding

arXiv: https://arxiv.org/abs/1706.06972 · HTML: https://mlsanity.com/paper/1706.06972/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2017.

## Built on by (most cited first, 5 of 5)

- [Guided Depth Map Super-resolution: A Survey](https://mlsanity.com/paper/2302.09598/) (2023)
- [Efficient ADMM-based Algorithms for Convolutional Sparse Coding](https://mlsanity.com/paper/2109.02969/) (2021)
- [An Efficient Approximate Method for Online Convolutional Dictionary Learning](https://mlsanity.com/paper/2301.10583/) (2023)
- [Online Sparse Synthetic Aperture Radar Imaging](https://mlsanity.com/paper/2603.08582/) (2026)
- [Convolutional Simultaneous Sparse Approximation with Applications to RGB-NIR Image Fusion](https://mlsanity.com/paper/2203.09913/) (2022)

## Abstract (arXiv)

Convolutional sparse coding (CSC) improves sparse coding by learning a shift-invariant dictionary from the data. However, existing CSC algorithms operate in the batch mode and are expensive, in terms of both space and time, on large datasets. In this paper, we alleviate these problems by using online learning. The key is a reformulation of the CSC objective so that convolution can be handled easily in the frequency domain and much smaller history matrices are needed. We use the alternating direction method of multipliers (ADMM) to solve the resulting optimization problem and the ADMM subproblems have efficient closed-form solutions. Theoretical analysis shows that the learned dictionary converges to a stationary point of the optimization problem. Extensive experiments show that convergence of the proposed method is much faster and its reconstruction performance is also better. Moreover, while existing CSC algorithms can only run on a small number of images, the proposed method can handle at least ten times more images.