A Survey of Sparse Representation: Algorithms and Applications

Zheng Zhang, Yong Xu, Jian Yang, Xuelong Li, Dapeng Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

896 Citations (Scopus)


Sparse representation has attracted much attention from researchers in fields of signal processing, image processing, computer vision, and pattern recognition. Sparse representation also has a good reputation in both theoretical research and practical applications. Many different algorithms have been proposed for sparse representation. The main purpose of this paper is to provide a comprehensive study and an updated review on sparse representation and to supply guidance for researchers. The taxonomy of sparse representation methods can be studied from various viewpoints. For example, in terms of different norm minimizations used in sparsity constraints, the methods can be roughly categorized into five groups: 1) sparse representation with $l-{0}$ -norm minimization; 2) sparse representation with $l-{p}$ -norm ( $0<p<1$ ) minimization; 3) sparse representation with $l-{1}$ -norm minimization; 4) sparse representation with $l-{2,1}$ -norm minimization; and 5) sparse representation with $l-{2}$ -norm minimization. In this paper, a comprehensive overview of sparse representation is provided. The available sparse representation algorithms can also be empirically categorized into four groups: 1) greedy strategy approximation; 2) constrained optimization; 3) proximity algorithm-based optimization; and 4) homotopy algorithm-based sparse representation. The rationales of different algorithms in each category are analyzed and a wide range of sparse representation applications are summarized, which could sufficiently reveal the potential nature of the sparse representation theory. In particular, an experimentally comparative study of these sparse representation algorithms was presented.
Original languageEnglish
Article number7102696
Pages (from-to)490-530
Number of pages41
JournalIEEE Access
Publication statusPublished - 1 Jan 2015


  • compressive sensing
  • constrained optimization
  • dictionary learning
  • greedy algorithm
  • homotopy algorithm
  • proximal algorithm
  • Sparse representation

ASJC Scopus subject areas

  • General Computer Science
  • General Materials Science
  • General Engineering


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