کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4605393 | 1337568 | 2011 | 9 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: New bounds on the restricted isometry constant δ2k New bounds on the restricted isometry constant δ2k](/preview/png/4605393.png)
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.
Journal: Applied and Computational Harmonic Analysis - Volume 31, Issue 3, November 2011, Pages 460-468