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CORR
2010
Springer

Restricted Isometries for Partial Random Circulant Matrices

11 years 9 months ago
Restricted Isometries for Partial Random Circulant Matrices
In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisition process that proceeds by convolution with a random pulse followed by (nonrandom) subsampling. At present, the theoretical analysis of this measurement technique is lacking. This paper demonstrates that the sth order restricted isometry constant is small when the number m of samples satisfies m (s log n)3/2 , where n is the length of the pulse. This bound improves on previous estimates, which exhibit quadratic scaling.
Holger Rauhut, Justin K. Romberg, Joel A. Tropp
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Holger Rauhut, Justin K. Romberg, Joel A. Tropp
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