# Convolutional Dictionary Learning: Acceleration and Convergence

arXiv: https://arxiv.org/abs/1707.00389 · HTML: https://mlsanity.com/paper/1707.00389/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2017.

## Built on by (most cited first, 6 of 6)

- [Provably Convergent Learned Inexact Descent Algorithm for Low-Dose CT Reconstruction](https://mlsanity.com/paper/2104.12939/) (2021)
- [Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction](https://mlsanity.com/paper/2412.13070/) (2024)
- [Model-based multi-parameter mapping](https://mlsanity.com/paper/2102.01604/) (2021)
- [Convolutional Analysis Operator Learning by End-To-End Training of Iterative Neural Networks](https://mlsanity.com/paper/2203.02166/) (2022)
- [Multi-Channel Convolutional Analysis Operator Learning for Dual-Energy CT Reconstruction](https://mlsanity.com/paper/2203.05968/) (2022)
- [Convolutional Dictionary Learning by End-To-End Training of Iterative Neural Networks](https://mlsanity.com/paper/2206.04447/) (2022)

## Abstract (arXiv)

Convolutional dictionary learning (CDL or sparsifying CDL) has many applications in image processing and computer vision. There has been growing interest in developing efficient algorithms for CDL, mostly relying on the augmented Lagrangian (AL) method or the variant alternating direction method of multipliers (ADMM). When their parameters are properly tuned, AL methods have shown fast convergence in CDL. However, the parameter tuning process is not trivial due to its data dependence and, in practice, the convergence of AL methods depends on the AL parameters for nonconvex CDL problems. To moderate these problems, this paper proposes a new practically feasible and convergent Block Proximal Gradient method using a Majorizer (BPG-M) for CDL. The BPG-M-based CDL is investigated with different block updating schemes and majorization matrix designs, and further accelerated by incorporating some momentum coefficient formulas and restarting techniques. All of the methods investigated incorporate a boundary artifacts removal (or, more generally, sampling) operator in the learning model. Numerical experiments show that, without needing any parameter tuning process, the proposed BPG-M approach converges more stably to desirable solutions of lower objective values than the existing state-of-the-art ADMM algorithm and its memory-efficient variant do. Compared to the ADMM approaches, the BPG-M method using a multi-block updating scheme is particularly useful in single-threaded CDL algorithm handling large datasets, due to its lower memory requirement and no polynomial computational complexity. Image denoising experiments show that, for relatively strong additive white Gaussian noise, the filters learned by BPG-M-based CDL outperform those trained by the ADMM approach.