A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
Convergence of the Gradient Projection Method for Generalized Convex Minimization
Computational Optimization and Applications
Algorithm 813: SPG—Software for Convex-Constrained Optimization
ACM Transactions on Mathematical Software (TOMS)
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication
SIAM Journal on Computing
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
SIAM Journal on Computing
Sparse representations are most likely to be the sparsest possible
EURASIP Journal on Applied Signal Processing
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Foundations of Computational Mathematics
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
An accelerated gradient method for trace norm minimization
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Sparsity preserving projections with applications to face recognition
Pattern Recognition
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
SIAM Journal on Optimization
Probing the Pareto Frontier for Basis Pursuit Solutions
SIAM Journal on Scientific Computing
Building sparse multiple-kernel SVM classifiers
IEEE Transactions on Neural Networks
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
Convergence properties of nonmonotone spectral projected gradient methods
Journal of Computational and Applied Mathematics
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Text detection in images using sparse representation with discriminative dictionaries
Image and Vision Computing
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Fixed point and Bregman iterative methods for matrix rank minimization
Mathematical Programming: Series A and B
Trace Norm Regularization: Reformulations, Algorithms, and Multi-Task Learning
SIAM Journal on Optimization
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
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Iterative hard thresholding (IHT) is a class of effective methods to compute sparse solution for underdetermined linear system. In this paper, an efficient IHT method with theoretical guarantee is proposed and named SCIHTBB with attractive features: (1) Monotone and Non-Monotone versions are presented with initial Barzilai-Borwein step size and finite step line search. (2) Convergence analysis has been developed based on the asymmetrical restricted isometry property. (3) An adaptive sparsity framework is provided to tackle the problem with unknown sparsity. (4) Some extensions are presented to handle group sparsity, non-negative sparsity and matrix rank minimization. Experimental comparisons with some state of the art methods verify that SCIHTBB is faster and more accurate for compressive sensing and matrix completion.