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Discrete Dynamics in Nature and Society
Volume 2013, Article ID 905027, 6 pages
Research Article

A Note on Block-Sparse Signal Recovery with Coherent Tight Frames

1School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
2School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received 23 May 2013; Accepted 17 November 2013

Academic Editor: Juan J. Nieto

Copyright © 2013 Yao Wang et al. 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 note discusses the recovery of signals from undersampled data in the situation that such signals are nearly block sparse in terms of an overcomplete and coherent tight frame . By introducing the notion of block -restricted isometry property (-RIP), we establish several sufficient conditions for the proposed mixed -analysis method to guarantee stable recovery of nearly block-sparse signals in terms of . One of the main results of this note shows that if the measurement matrix satisfies the block -RIP with constants , then the signals which are nearly block -sparse in terms of can be stably recovered via mixed -analysis in the presence of noise.