Comparing measures of sparsity
IEEE Transactions on Information Theory
Minimizing nonconvex functions for sparse vector reconstruction
IEEE Transactions on Signal Processing
Blind extraction of global signal from multi-channel noisy observations
IEEE Transactions on Neural Networks
Sound field reproduction using the Lasso
IEEE Transactions on Audio, Speech, and Language Processing
Sparsity-aware estimation of CDMA system parameters
EURASIP Journal on Advances in Signal Processing - Special issue on advanced equalization techniques for wireless communications
The Journal of Machine Learning Research
Sparse Signal Reconstruction via Iterative Support Detection
SIAM Journal on Imaging Sciences
A coordinate gradient descent method for l1-regularized convex minimization
Computational Optimization and Applications
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
Robust visual tracking with structured sparse representation appearance model
Pattern Recognition
Face recognition using discriminant sparsity neighborhood preserving embedding
Knowledge-Based Systems
Efficient point-to-subspace query in ℓ1 with application to robust face recognition
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
Comparing L1 and L2 distances for CTA
PSD'12 Proceedings of the 2012 international conference on Privacy in Statistical Databases
Real-time classification via sparse representation in acoustic sensor networks
Proceedings of the 11th ACM Conference on Embedded Networked Sensor Systems
Compressed sensing signal recovery via forward-backward pursuit
Digital Signal Processing
Adaptive all-season image tag ranking by saliency-driven image pre-classification
Journal of Visual Communication and Image Representation
Hi-index | 754.90 |
The minimum lscr1-norm solution to an underdetermined system of linear equations y=Ax is often, remarkably, also the sparsest solution to that system. This sparsity-seeking property is of interest in signal processing and information transmission. However, general-purpose optimizers are much too slow for lscr1 minimization in many large-scale applications.In this paper, the Homotopy method, originally proposed by Osborne et al. and Efron et al., is applied to the underdetermined lscr1-minimization problem min parxpar1 subject to y=Ax. Homotopy is shown to run much more rapidly than general-purpose LP solvers when sufficient sparsity is present. Indeed, the method often has the following k-step solution property: if the underlying solution has only k nonzeros, the Homotopy method reaches that solution in only k iterative steps. This k-step solution property is demonstrated for several ensembles of matrices, including incoherent matrices, uniform spherical matrices, and partial orthogonal matrices. These results imply that Homotopy may be used to rapidly decode error-correcting codes in a stylized communication system with a computational budget constraint. The approach also sheds light on the evident parallelism in results on lscr1 minimization and orthogonal matching pursuit (OMP), and aids in explaining the inherent relations between Homotopy, least angle regression (LARS), OMP, and polytope faces pursuit.