Algorithm 890: Sparco: A Testing Framework for Sparse Reconstruction
ACM Transactions on Mathematical Software (TOMS)
Nonlinear regularization techniques for seismic tomography
Journal of Computational Physics
Stagewise weak gradient pursuits
IEEE Transactions on Signal Processing
Sparsity inspired selection and recognition of iris images
BTAS'09 Proceedings of the 3rd IEEE international conference on Biometrics: Theory, applications and systems
Sparse approximate solution of partial differential equations
Applied Numerical Mathematics
Basis pursuit for robust passive acoustic beamforming
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Projected Landweber iteration for matrix completion
Journal of Computational and Applied Mathematics
Compressive acquisition of dynamic scenes
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part I
Dictionary learning for sparse representations: a Pareto curve root finding approach
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
SMALLbox - an evaluation framework for sparse representations and dictionary learning algorithms
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Two-dimensional random projection
Signal Processing
A non-adapted sparse approximation of PDEs with stochastic inputs
Journal of Computational Physics
SIAM Journal on Scientific Computing
International Journal of Sensor Networks
Generalized sparse regularization with application to fMRI brain decoding
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Compressed sensing of complex-valued data
Signal Processing
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
SIAM Journal on Scientific Computing
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
A First-Order Smoothed Penalty Method for Compressed Sensing
SIAM Journal on Optimization
A Regularization Parameter for Nonsmooth Tikhonov Regularization
SIAM Journal on Scientific Computing
Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Codes
SIAM Journal on Imaging Sciences
Optimized projection for sparse representation based classification
ICIC'11 Proceedings of the 7th international conference on Advanced Intelligent Computing
Numerical methods for A-optimal designs with a sparsity constraint for ill-posed inverse problems
Computational Optimization and Applications
Journal of Mathematical Imaging and Vision
Minimizing Condition Number via Convex Programming
SIAM Journal on Matrix Analysis and Applications
SAR image reconstruction and autofocus by compressed sensing
Digital Signal Processing
Two systems for automatic music genre recognition: what are they really recognizing?
Proceedings of the second international ACM workshop on Music information retrieval with user-centered and multimodal strategies
Fast multi-contrast MRI reconstruction
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Sparse Doppler-only snapshot imaging for space debris
Signal Processing
Accelerated Linearized Bregman Method
Journal of Scientific Computing
A cyclic projected gradient method
Computational Optimization and Applications
Computational Optimization and Applications
Digital paparazzi: spotting celebrities in professional photo libraries
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part II
Compressed sensing photoacoustic imaging based on fast alternating direction algorithm
Journal of Biomedical Imaging
Exact sparse recovery with L0 projections
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Robust and efficient iris recognition based on sparse error correction model
ICIC'13 Proceedings of the 9th international conference on Intelligent Computing Theories
Large-scale multilabel propagation based on efficient sparse graph construction
ACM Transactions on Multimedia Computing, Communications, and Applications (TOMCCAP)
Structured Sparsity Models for Reverberant Speech Separation
IEEE/ACM Transactions on Audio, Speech and Language Processing (TASLP)
Homogeneous Penalizers and Constraints in Convex Image Restoration
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Classification accuracy is not enough
Journal of Intelligent Information Systems
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The basis pursuit problem seeks a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise (BPDN) fits the least-squares problem only approximately, and a single parameter determines a curve that traces the optimal trade-off between the least-squares fit and the one-norm of the solution. We prove that this curve is convex and continuously differentiable over all points of interest, and show that it gives an explicit relationship to two other optimization problems closely related to BPDN. We describe a root-finding algorithm for finding arbitrary points on this curve; the algorithm is suitable for problems that are large scale and for those that are in the complex domain. At each iteration, a spectral gradient-projection method approximately minimizes a least-squares problem with an explicit one-norm constraint. Only matrix-vector operations are required. The primal-dual solution of this problem gives function and derivative information needed for the root-finding method. Numerical experiments on a comprehensive set of test problems demonstrate that the method scales well to large problems.