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The restricted isometry property for time-frequency structured random matrices.
- Source :
- Probability Theory & Related Fields; Aug2013, Vol. 156 Issue 3/4, p707-737, 31p
- Publication Year :
- 2013
-
Abstract
- This paper establishes the restricted isometry property for a Gabor system generated by n time-frequency shifts of a random window function in n dimensions. The sth order restricted isometry constant of the associated n × n Gabor synthesis matrix is small provided that s ≤ c n / log n. This bound provides a qualitative improvement over previous estimates, which achieve only quadratic scaling of the sparsity s with respect to n. The proof depends on an estimate for the expected supremum of a second-order chaos. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01788051
- Volume :
- 156
- Issue :
- 3/4
- Database :
- Complementary Index
- Journal :
- Probability Theory & Related Fields
- Publication Type :
- Academic Journal
- Accession number :
- 89078788
- Full Text :
- https://doi.org/10.1007/s00440-012-0441-4