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On the Theorem of Uniform Recovery of Random Sampling Matrices by Andersson, Joel; Strömberg, Jan-Olov is a scholarly article available to read on EtoBox.

What is On the Theorem of Uniform Recovery of Random Sampling Matrices about?

We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an $s$-sparse signal from linear measurements (with high probability) is known to be $m\gtrsim s(\ln s)^3\ln N$. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of $m\times N$-matrices, by considering what we call \emph{low entropy}. We also present an improved condition on the so-called restricted isometry constants, $\delta_s$, ensuring sparse recovery via $\ell^1$-minimization. We show that $\delta_{2s}<4/\sqrt{41}$ is sufficient and that this can be improved further to almost allow for a sufficient condition of the type $\delta_{2s}<2/3$.

Author

Andersson, Joel; Strömberg, Jan-Olov

Published

2012

Language

EN