# New Bounds for Restricted Isometry Constants - Computer Science > Information Theory

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Abstract: In this paper we show that if the restricted isometry constant $\delta k$ ofthe compressed sensing matrix satisfies \ \delta k < 0.307, \ then $k$-sparsesignals are guaranteed to be recovered exactly via $\ell 1$ minimization whenno noise is present and $k$-sparse signals can be estimated stably in the noisycase. It is also shown that the bound cannot be substantively improved. Anexplicitly example is constructed in which $\delta {k}=\frac{k-1}{2k-1} < 0.5$,but it is impossible to recover certain $k$-sparse signals.

Author: ** T. Tony Cai, Lie Wang, Guangwu Xu**

Source: https://arxiv.org/