# Convolutional Dictionary Learning: A Comparative Review and New Algorithms

arXiv: https://arxiv.org/abs/1709.02893 · HTML: https://mlsanity.com/paper/1709.02893/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2017.

## Built on by (most cited first, 23 of 23)

- [Revisiting Multimodal Representation in Contrastive Learning: From Patch and Token Embeddings to Finite Discrete Tokens](https://mlsanity.com/paper/2303.14865/) (2023)
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- [Heterogeneous Domain Adaptation with Adversarial Neural Representation Learning: Experiments on E-Commerce and Cybersecurity](https://mlsanity.com/paper/2205.07853/) (2022)
- [Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction](https://mlsanity.com/paper/2412.13070/) (2024)
- [Unrolled Compressed Blind-Deconvolution](https://mlsanity.com/paper/2209.14165/) (2022)
- [Personalized Convolutional Dictionary Learning of Physiological Time Series](https://mlsanity.com/paper/2503.07687/) (2025)
- [Learning Spatially Adaptive ℓ1-Norms Weights for Convolutional Synthesis Regularization](https://mlsanity.com/paper/2503.09483/) (2025)
- [Gaussian Process Convolutional Dictionary Learning](https://mlsanity.com/paper/2104.00530/) (2021)
- [Adaptive Clustering of Robust Semantic Representations for Adversarial Image Purification](https://mlsanity.com/paper/2104.02155/) (2021)
- [An Efficient Approximate Method for Online Convolutional Dictionary Learning](https://mlsanity.com/paper/2301.10583/) (2023)
- [Multi-dimensional Signal Recovery using Low-rank Deconvolution](https://mlsanity.com/paper/2305.02264/) (2023)
- [Dictionary Learning under Symmetries via Group Representations](https://mlsanity.com/paper/2305.19557/) (2023)
- [Robust Foreground-Background Separation for Severely-Degraded Videos Using Convolutional Sparse Representation Modeling](https://mlsanity.com/paper/2506.17838/) (2025)
- [Learning spatially adaptive sparsity level maps for arbitrary convolutional dictionaries](https://mlsanity.com/paper/2602.21707/) (2026)
- [Fast Unsupervised Tensor Restoration via Low-rank Deconvolution](https://mlsanity.com/paper/2406.10679/) (2024)
- [Robust online reconstruction of continuous-time signals from a lean spike train ensemble code](https://mlsanity.com/paper/2408.05950/) (2024)
- [YOLO-RD: Introducing Relevant and Compact Explicit Knowledge to YOLO by Retriever-Dictionary](https://mlsanity.com/paper/2410.15346/) (2024)
- [Latent Mode Decomposition](https://mlsanity.com/paper/2505.17797/) (2025)
- [Efficient Chambolle-Pock based algorithms for Convoltional sparse representation](https://mlsanity.com/paper/2508.02152/) (2025)
- [Convolutional Sparse Coding via the Locally Competitive Algorithm on Loihi 2](https://mlsanity.com/paper/2606.08584/) (2026)

## Abstract (arXiv)

Convolutional sparse representations are a form of sparse representation with a dictionary that has a structure that is equivalent to convolution with a set of linear filters. While effective algorithms have recently been developed for the convolutional sparse coding problem, the corresponding dictionary learning problem is substantially more challenging. Furthermore, although a number of different approaches have been proposed, the absence of thorough comparisons between them makes it difficult to determine which of them represents the current state of the art. The present work both addresses this deficiency and proposes some new approaches that outperform existing ones in certain contexts. A thorough set of performance comparisons indicates a very wide range of performance differences among the existing and proposed methods, and clearly identifies those that are the most effective.