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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 4372080, 8 pages
Research Article

Improved RIP Conditions for Compressed Sensing with Coherent Tight Frames

1School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
2Shenyang Institute of Automation, Chinese Academy of Science, Shenyang 10016, China
3School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Correspondence should be addressed to Jianjun Wang; nc.ude.uws@jjw

Received 1 February 2017; Accepted 12 April 2017; Published 15 May 2017

Academic Editor: Daniele Fournier-Prunaret

Copyright © 2017 Yao Wang and Jianjun Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper establishes new sufficient conditions on the restricted isometry property (RIP) for compressed sensing with coherent tight frames. One of our main results shows that the RIP (adapted to ) condition guarantees the stable recovery of all signals that are nearly -sparse in terms of a coherent tight frame via the -analysis method, which improves the existing ones in the literature.