# Efficient ADMM-based Algorithms for Convolutional Sparse Coding

arXiv: https://arxiv.org/abs/2109.02969 · HTML: https://mlsanity.com/paper/2109.02969/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 30 references that are in the map.
- First posted on arXiv 7 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Convolutional Dictionary Learning: A Comparative Review and New Algorithms](https://mlsanity.com/paper/1709.02893/) (2017)
- [Convolutional Dictionary Learning via Local Processing](https://mlsanity.com/paper/1705.03239/) (2017)
- [Convolutional Sparse Coding for Compressed Sensing CT Reconstruction](https://mlsanity.com/paper/1903.08549/) (2019)
- [Scalable Online Convolutional Sparse Coding](https://mlsanity.com/paper/1706.06972/) (2017)
- [Coupled Feature Learning for Multimodal Medical Image Fusion](https://mlsanity.com/paper/2102.08641/) (2021)
- [PSF Estimation in Crowded Astronomical Imagery as a Convolutional Dictionary Learning Problem](https://mlsanity.com/paper/2101.01268/) (2021)

## Built on by (most cited first, 4 of 4)

- [An Efficient Approximate Method for Online Convolutional Dictionary Learning](https://mlsanity.com/paper/2301.10583/) (2023)
- [Convolutional Simultaneous Sparse Approximation with Applications to RGB-NIR Image Fusion](https://mlsanity.com/paper/2203.09913/) (2022)
- [Framework Construction of an Adversarial Federated Transfer Learning Classifier](https://mlsanity.com/paper/2211.04734/) (2022)
- [Efficient Chambolle-Pock based algorithms for Convoltional sparse representation](https://mlsanity.com/paper/2508.02152/) (2025)

## Abstract (arXiv)

Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers and the convolution theorem. The only major difference between these methods is how they approach a convolutional least-squares fitting subproblem. This letter presents a solution to this subproblem, which improves the efficiency of the state-of-the-art algorithms. We also use the same approach for developing an efficient convolutional dictionary learning method. Furthermore, we propose a novel algorithm for convolutional sparse coding with a constraint on the approximation error.