IEEE Access· 2015Q1· Review
A Survey of Sparse Representation: Algorithms and Applications
- 1,089citations
- Q1SCImago
- 2015year
Short summary
This survey provides a comprehensive review of sparse representation techniques, categorizing algorithms by norm minimization (l0, lp, l1, l2,1, l2) and algorithmic approach (greedy, constrained optimization, proximity, homotopy).
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Key points
- Sparse representation algorithms are categorized by norm minimization: l0, lp (0<p<1), l1, l2,1, and l2.
- Algorithmic approaches include greedy strategies, constrained optimization, proximity algorithms, and homotopy algorithms.
- The paper analyzes the theoretical basis and practical applications of various sparse representation methods.
- An experimental comparative study of these algorithms is presented.
AI-generated from the title and abstract; the full text is not read.
Abstract
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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm minimization; 2) sparse representation with lp-norm (0 <; p <; 1) minimization; 3) sparse representation with l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm minimization; 4) sparse representation with l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,1-norm minimization; and 5) sparse representation with l2-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.
The authors' abstract, as published at the source. IEEE Access, 2015 · DOI ↗
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Field: Computational Mechanics
Computational MechanicsEngineering