New bounds on the restricted isometry constant δ2k

Restricted isometry constants play an important role in compressed sensing. In the literature, E.J. Candès has proven that is a sufficient condition for the l1 minimization problem having a k-sparse solution. Later, S. Foucart and M. Lai have improved the condition to δ2k<0.4531 and S. Foucart has improved the bound to δ2k<0.4652. In 2010, T. Cai, L. Wang and G. Xu have improved the condition to δ2k<0.4721 for the cases such that k is a multiple of 4 or k is very large and S. Foucart has improved the bound to δ2k<0.4734 for large values of k. In this paper, we have improved the sufficient condition to δ2k<0.4931 for general k. Also, in some special cases, the sufficient condition can be improved to δ2k<0.6569. These new bounds have several benefits on recovering compressible signals with noise.