Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Atomic Decomposition by Basis Pursuit
SIAM Review
Approximation of functions over redundant dictionaries using coherence
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On Lebesgue-type inequalities for greedy approximation
Journal of Approximation Theory
Decoding by linear programming
IEEE Transactions on Information Theory
Journal of Approximation Theory
Unit time-phase signal sets: Bounds and constructions
Cryptography and Communications
| Hi-index | 0.00 |
This paper concerns systems with small coherence parameter. Simple greedy-type algorithms perform well on these systems, which are also useful in the construction of compressed sensing matrices. We discuss the following problems for both R^n and C^n. How large can a dictionary be, if we prescribe the coherence parameter? How small could the resulting coherence parameter be, if we impose a size on the dictionary? How could we construct such a system? Several fundamental results from different areas of mathematics shed light on these important problems with far-reaching implications in approximation theory.