A Survey of Sparse Representation: Algorithms and Applications
TLDR
A comprehensive overview of sparse representation is provided and an experimentally comparative study of these sparse representation algorithms was presented, which could sufficiently reveal the potential nature of the sparse representation theory.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 $l_{0}$ -norm minimization; 2) sparse representation with $l_{p}$ -norm ( $0 ) 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.read more
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References
More filters
Journal ArticleDOI
Regression Shrinkage and Selection via the Lasso
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
Book
Convex Optimization
Stephen Boyd,Lieven Vandenberghe +1 more
TL;DR: In this article, the focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them, and a comprehensive introduction to the subject is given. But the focus of this book is not on the optimization problem itself, but on the problem of finding the appropriate technique to solve it.
Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Book
Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers
TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.