A Survey of Sparse Representation: Algorithms and Applications

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 article is to provide a comprehensive study and an updated review on sparse representation and to supply a 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: sparse representation with l0-norm minimization, sparse representation with lp-norm (0<p<1) minimization, sparse representation with l1-norm minimization, sparse representation with l2,1-norm minimization, and 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: greedy strategy approximation, constrained optimization, proximity algorithm-based optimization, and 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. Specifically, an experimentally comparative study of these sparse representation algorithms was presented.

Image Super-Resolution via Wavelet Feature Extraction and Sparse Representation

“…A Gaussian filter of size 3×3 with standard deviation 0.5 followed by downsampling by a scale factor of S = 2. The first scenario was used to super-resolve the standard images and the aerial images, and the second scenario was used according to the medical SR simulations presented in [13]. The DWT employed to extract features was the CDF 9/7 WT [32], the trained dictionaries (D h and D l ) have 25×1024 atoms.…”

“…The learning methods learn prior knowledge using databases and this prior knowledge is incorporated during the reconstruction process [13]. In the stateof-the-art methods, there are pioneering works that use sparse representation to solve the inverse problem presented in (1).…”

Virtual Samples Construction Using Image-Block-Stretching for Face Recognition

“…Representation algorithms with the l 2 minimization have analytic solutions whereas conventional SRC algorithms should use iterative procedures to determine the solutions. Moreover, the formers always have lower computational costs than the conventional SRC algorithm [26].…”

Dynamic dictionary optimization for sparse-representation-based face classification using local difference images

“…In contrast with traditional 5 methods [4,19,24,25,26,27,55,60], sparse representation has introduced a number of new methodologies with promising results to the aforementioned areas. A survey of sparse representation and its applications is presented in [59]. For pattern recognition and classification, the most well-known sparse representation method is believed to be sparse-representation-based classification (SRC) [43,44], which performs classi-samples by performing image perturbation on original samples.…”