A Survey of Sparse Representation: Algorithms and Applications

Zheng Zhang (1, 2) , Yong Xu (1, 2) , Jian Yang (3) , Xuelong Li (4) , David Zhang (5)

1 Bio-Computing Research Center
2 Key Laboratory of Network Oriented Intelligent Computation
3 College of Computer Science and Technology
4 State Key Laboratory of Transient Optics and Photonics
5 Biometrics Research Center

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.

Mots clés: dictionary learning; compressive sensing; sparse representation; greedy algorithm; constrained optimization; proximal algorithm; homotopy algorithm

Domaines: Sciences de l'ingénieur [physics]

Zheng Zhang, Yong Xu, Jian Yang, Xuelong Li, David Zhang. A Survey of Sparse Representation: Algorithms and Applications . IEEE Access, 2015, ⟨10.1109/ACCESS.2015.2430359⟩. ⟨hal-01311245⟩