Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Approximation Numbers (1)
- Basis pursuit (1)
- Bernstein Pairs (1)
- Bernstein's Theorem (1)
- Compressed sensing (1)
-
- Diagonal Operators (1)
- Fubini's theorem (1)
- Mean Value Theorem (1)
- Mixed partial derivatives (1)
- Order of integration (1)
- Orthogonal matching pursuit (1)
- Restricted isometry condition (1)
- S-Numbers (1)
- Signal recovery (1)
- Signal recovery algorithms (1)
- Sparse approximation (1)
- Uncertainty principle (1)
Articles 1 - 3 of 3
Full-Text Articles in Mathematics
Uniform Uncertainty Principle And Signal Recovery Via Regularized Orthogonal Matching Pursuit, Deanna Needell, Roman Vershynin
Uniform Uncertainty Principle And Signal Recovery Via Regularized Orthogonal Matching Pursuit, Deanna Needell, Roman Vershynin
CMC Faculty Publications and Research
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-minimization. Our algorithm, ROMP, reconstructs a sparse signal in a number of iterations linear in the sparsity, and the reconstruction is exact provided the linear measurements satisfy the uniform uncertainty principle.
Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli
Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli
CMC Faculty Publications and Research
A most fascinating aspect of calculus is its power to surprise even an experienced mathemat ician. Just when it appears that all ideas, results and connections have been discovered and thorough ly analyzed, the horizon suddenly broadens and somebody cries the familiar "eureka". The reason could be either a new result, a simpler way to prove an existing theorem, or a previously missed connection between different ideas. This potential for enrichment is second to none, and it reaffirms the unparalleled educational value of this area of mathematics.
Diagonal Operators, S-Numbers, And Bernstein Pairs, Asuman Güven Aksoy, Grzegorz Lewicki
Diagonal Operators, S-Numbers, And Bernstein Pairs, Asuman Güven Aksoy, Grzegorz Lewicki
CMC Faculty Publications and Research
Replacing the nested sequence of ''finite" dimensional subspaces by the nested sequence of "closed" subspaces in the classical Bernstein lethargy theorem, we obtain a version of this theorem for the space B(X , Y) of all bounded linear maps. Using this result and some properties of diagonal operators, we investigate conditions under which a suitable pair of Banach spaces form an exact Bernstein pair.We also show that many "classical" Banach spaces, including the couple (Lp [O, 1] , Lq[O, 1]) form a Bernstein pair with respect to any sequence of s-numbers (sn) ,for 1 < p < ∞ and 1 ≤ q < ∞ …