---
title: "Exact Recovery of Sparse-Used Dictionaries"
authors:
  - "Huan Wang"
  - "Daniel A. Spielman"
  - "John Wright"
doi: ""
url: "https://ijcai.org/proceedings/2013/462"
pdf: "https://ijcai.org/proceedings/2013/0462.pdf"
venue: "Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence"
year: 2013
pages: "3087-3089"
track: ""
keywords:
---

# Exact Recovery of Sparse-Used Dictionaries

Huan Wang, Daniel A. Spielman, John Wright

*Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence*, pages 3087-3089.

## Abstract

We consider the problem of learning sparsely used dictionaries with an arbitrary square dictionary and a random, sparse coefficient matrix. We prove that O (n log n) samples are sufficient to uniquely determine the coefficient matrix. Based on this proof, we design a polynomial-time algorithm, called Exact Recovery of Sparsely-Used Dictionaries (ER-SpUD), and prove that it probably recovers the dictionary and coefficient matrix when the coefficient matrix is sufficiently sparse. Simulation results show that ER-SpUD reveals the true dictionary as well as the coefficients with probability higher than many state-of-the-art algorithms.