# Convolutional Dictionary Learning via Local Processing

arXiv: https://arxiv.org/abs/1705.03239 · HTML: https://mlsanity.com/paper/1705.03239/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2017.

## Built on by (most cited first, 19 of 19)

- [LRRNet: A Novel Representation Learning Guided Fusion Network for Infrared and Visible Images](https://mlsanity.com/paper/2304.05172/) (2023)
- [Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Models](https://mlsanity.com/paper/2502.12892/) (2025)
- [Universal Sparse Autoencoders: Interpretable Cross-Model Concept Alignment](https://mlsanity.com/paper/2502.03714/) (2025)
- [ISCL: Interdependent Self-Cooperative Learning for Unpaired Image Denoising](https://mlsanity.com/paper/2102.09858/) (2021)
- [Optimal Regularization for a Data Source](https://mlsanity.com/paper/2212.13597/) (2022)
- [Efficient ADMM-based Algorithms for Convolutional Sparse Coding](https://mlsanity.com/paper/2109.02969/) (2021)
- [Adversarial Distortion Learning for Medical Image Denoising](https://mlsanity.com/paper/2204.14100/) (2022)
- [A New Look at Spike-Timing-Dependent Plasticity Networks for Spatio-Temporal Feature Learning](https://mlsanity.com/paper/2111.00791/) (2021)
- [Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction](https://mlsanity.com/paper/2412.13070/) (2024)
- [l0-Regularized Sparse Coding-based Interpretable Network for Multi-Modal Image Fusion](https://mlsanity.com/paper/2411.04519/) (2024)
- [Convolutional Dictionary Learning by End-To-End Training of Iterative Neural Networks](https://mlsanity.com/paper/2206.04447/) (2022)
- [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)
- [Improved Image Generation via Sparse Modeling](https://mlsanity.com/paper/2104.00464/) (2021)
- [WSEBP: A Novel Width-depth Synchronous Extension-based Basis Pursuit Algorithm for Multi-Layer Convolutional Sparse Coding](https://mlsanity.com/paper/2203.14856/) (2022)
- [Fast Unsupervised Tensor Restoration via Low-rank Deconvolution](https://mlsanity.com/paper/2406.10679/) (2024)
- [Efficient Chambolle-Pock based algorithms for Convoltional sparse representation](https://mlsanity.com/paper/2508.02152/) (2025)
- [RoseCDL: Robust and Scalable Convolutional Dictionary Learning for Rare event and Anomaly Detection](https://mlsanity.com/paper/2509.07523/) (2025)

## Abstract (arXiv)

Convolutional Sparse Coding (CSC) is an increasingly popular model in the signal and image processing communities, tackling some of the limitations of traditional patch-based sparse representations. Although several works have addressed the dictionary learning problem under this model, these relied on an ADMM formulation in the Fourier domain, losing the sense of locality and the relation to the traditional patch-based sparse pursuit. A recent work suggested a novel theoretical analysis of this global model, providing guarantees that rely on a localized sparsity measure. Herein, we extend this local-global relation by showing how one can efficiently solve the convolutional sparse pursuit problem and train the filters involved, while operating locally on image patches. Our approach provides an intuitive algorithm that can leverage standard techniques from the sparse representations field. The proposed method is fast to train, simple to implement, and flexible enough that it can be easily deployed in a variety of applications. We demonstrate the proposed training scheme for image inpainting and image separation, while achieving state-of-the-art results.