Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Reproducible Research in Computational Harmonic Analysis
Computing in Science and Engineering
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
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
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
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
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A fast and accurate first-order algorithm for compressed sensing
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Fast image recovery using variable splitting and constrained optimization
IEEE Transactions on Image Processing
SIAM Journal on Scientific Computing
A fast and exact algorithm for total variation minimization
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part I
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
Fast Solution of -Norm Minimization Problems When the Solution May Be Sparse
IEEE Transactions on Information Theory
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
IEEE Transactions on Image Processing
IEEE Transactions on Information Theory
Restoration of images based on subspace optimization accelerating augmented Lagrangian approach
Journal of Computational and Applied Mathematics
Robust principal component analysis?
Journal of the ACM (JACM)
International Journal of Sensor Networks
Deconvolving Poissonian images by a novel hybrid variational model
Journal of Visual Communication and Image Representation
Compressed sensing of complex-valued data
Signal Processing
Towards multi-semantic image annotation with graph regularized exclusive group lasso
MM '11 Proceedings of the 19th ACM international conference on Multimedia
Gradient-Based Methods for Sparse Recovery
SIAM Journal on Imaging Sciences
A First-Order Smoothed Penalty Method for Compressed Sensing
SIAM Journal on Optimization
SIAM Journal on Imaging Sciences
A compressive sensing scheme of frequency sparse signals for mobile and wearable platforms
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part II
Continuous Multiclass Labeling Approaches and Algorithms
SIAM Journal on Imaging Sciences
Computational Optimization and Applications
Image representation using block compressive sensing for compression applications
Journal of Visual Communication and Image Representation
Sparse signal reconstruction using decomposition algorithm
Knowledge-Based Systems
Nesterov's algorithm solving dual formulation for compressed sensing
Journal of Computational and Applied Mathematics
Nonparametric sparsity and regularization
The Journal of Machine Learning Research
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Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. This paper applies a smoothing technique and an accelerated first-order algorithm, both from Nesterov [Math. Program. Ser. A, 103 (2005), pp. 127-152], and demonstrates that this approach is ideally suited for solving large-scale compressed sensing reconstruction problems as (1) it is computationally efficient, (2) it is accurate and returns solutions with several correct digits, (3) it is flexible and amenable to many kinds of reconstruction problems, and (4) it is robust in the sense that its excellent performance across a wide range of problems does not depend on the fine tuning of several parameters. Comprehensive numerical experiments on realistic signals exhibiting a large dynamic range show that this algorithm compares favorably with recently proposed state-of-the-art methods. We also apply the algorithm to solve other problems for which there are fewer alternatives, such as total-variation minimization and convex programs seeking to minimize the $\ell_1$ norm of $Wx$ under constraints, in which $W$ is not diagonal. The code is available online as a free package in the MATLAB language.