Resolution Improvement of Scanning Acoustic Microscopy Using Sparse Signal Representation
Journal of Signal Processing Systems
Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
Stagewise weak gradient pursuits
IEEE Transactions on Signal Processing
Monotone operator splitting for optimization problems in sparse recovery
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
PCM'10 Proceedings of the Advances in multimedia information processing, and 11th Pacific Rim conference on Multimedia: Part II
SIAM Journal on Scientific Computing
Sparse Signal Reconstruction via Iterative Support Detection
SIAM Journal on Imaging Sciences
Compressed sensing for efficient random routing in multi-hop wireless sensor networks
International Journal of Communication Networks and Distributed Systems
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
SIAM Journal on Imaging Sciences
Sparsity lower bounds for dimensionality reducing maps
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Compressed sensing signal recovery via forward-backward pursuit
Digital Signal Processing
Hi-index | 754.84 |
Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard in general. We show here that for systems with “typical”/“random” Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our proposal, Stagewise Orthogonal Matching Pursuit (StOMP), successively transforms the signal into a negligible residual. Starting with initial residual r0 = y, at the s -th stage it forms the “matched filter” ΦTrs-1, identifies all coordinates with amplitudes exceeding a specially chosen threshold, solves a least-squares problem using the selected coordinates, and subtracts the least-squares fit, producing a new residual. After a fixed number of stages (e.g., 10), it stops. In contrast to Orthogonal Matching Pursuit (OMP), many coefficients can enter the model at each stage in StOMP while only one enters per stage in OMP; and StOMP takes a fixed number of stages (e.g., 10), while OMP can take many (e.g., n). We give both theoretical and empirical support for the large-system effectiveness of StOMP. We give numerical examples showing that StOMP rapidly and reliably finds sparse solutions in compressed sensing, decoding of error-correcting codes, and overcomplete representation.