# Analysis of Fast Structured Dictionary Learning

arXiv: https://arxiv.org/abs/1805.12529 · HTML: https://mlsanity.com/paper/1805.12529/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2018.

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

- [Simple Alternating Minimization Provably Solves Complete Dictionary Learning](https://mlsanity.com/paper/2210.12816/) (2022)
- [Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond](https://mlsanity.com/paper/2103.14528/) (2021)
- [Personalized Dictionary Learning for Heterogeneous Datasets](https://mlsanity.com/paper/2305.15311/) (2023)
- [Personalized Convolutional Dictionary Learning of Physiological Time Series](https://mlsanity.com/paper/2503.07687/) (2025)
- [Enhancing Performance of Explainable AI Models with Constrained Concept Refinement](https://mlsanity.com/paper/2502.06775/) (2025)

## Abstract (arXiv)

Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can outperform analytical models. In particular, alternating optimization algorithms have been popular for learning such models. In this work, we focus on alternating minimization for a specific structured unitary sparsifying operator learning problem, and provide a convergence analysis. While the algorithm converges to the critical points of the problem generally, our analysis establishes under mild assumptions, the local linear convergence of the algorithm to the underlying sparsifying model of the data. Analysis and numerical simulations show that our assumptions hold for standard probabilistic data models. In practice, the algorithm is robust to initialization.