Superresolution via sparsity constraints
SIAM Journal on Mathematical Analysis
Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Improvements on bottleneck matching and related problems using geometry
Proceedings of the twelfth annual symposium on Computational geometry
Atomic Decomposition by Basis Pursuit
SIAM Review
Approximate congruence in nearly linear time
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
CoSaMP: iterative signal recovery from incomplete and inaccurate samples
Communications of the ACM
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Stable recovery of sparse overcomplete representations in the presence of noise
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
Stability Results for Random Sampling of Sparse Trigonometric Polynomials
IEEE Transactions on Information Theory
A Probabilistic and RIPless Theory of Compressed Sensing
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
Highly coherent sensing matrices arise in discretization of continuum imaging problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold. Algorithms based on techniques of band exclusion (BE) and local optimization (LO) are proposed to deal with such coherent sensing matrices. These techniques are embedded in the existing compressed sensing algorithms, such as Orthogonal Matching Pursuit (OMP), Subspace Pursuit (SP), Iterative Hard Thresholding (IHT), Basis Pursuit (BP), and Lasso, and result in the modified algorithms BLOOMP, BLOSP, BLOIHT, BP-BLOT, and Lasso-BLOT, respectively. Under appropriate conditions, it is proved that BLOOMP can reconstruct sparse, widely separated objects up to one Rayleigh length in the Bottleneck distance independent of the grid spacing. One of the most distinguishing attributes of BLOOMP is its capability of dealing with large dynamic ranges. The BLO-based algorithms are systematically tested with respect to four performance metrics: dynamic range, noise stability, sparsity, and resolution. With respect to dynamic range and noise stability, BLOOMP is the best performer. With respect to sparsity, BLOOMP is the best performer for high dynamic range, while for dynamic range near unity BP-BLOT and Lasso-BLOT with the optimized regularization parameter have the best performance. In the noiseless case, BP-BLOT has the highest resolving power up to certain dynamic range. The algorithms BLOSP and BLOIHT are good alternatives to BLOOMP and BP/Lasso-BLOT: they are faster than both BLOOMP and BP/Lasso-BLOT and share, to a lesser degree, BLOOMP's amazing attribute with respect to dynamic range. Detailed comparisons with the algorithms Spectral Iterative Hard Thresholding (SIHT) and the frame-adapted BP demonstrate the superiority of the BLO-based algorithms for the problem of sparse approximation in terms of highly coherent, redundant dictionaries.