Linear convergence of adaptively iterative thresholding algorithms for compressed sensing

Yu Wang Xi'an Jiaotong University Jinshan Zeng Xi'an Jiaotong University Zhimin Peng UCLA Xiangyu Chang Xi'an Jiaotong University Zongben Xu Xi'an Jiaotong University

Optimization and Control mathscidoc:1701.27011

Best Paper Award in 2018

This paper studies the convergence of the adaptively iterative thresholding (AIT) algorithm for compressed sensing. We first introduce a generalized restricted isometry property (gRIP). Then, we prove that the AIT algorithm converges to the original sparse solution at a linear rate under a certain gRIP condition in the noise free case. While in the noisy case, its convergence rate is also linear until attaining a certain error bound. Moreover, as by-products, we also provide some sufficient conditions for the convergence of the AIT algorithm based on the two well-known properties, i.e., the coherence property and the restricted isometry property (RIP), respectively. It should be pointed out that such two properties are special cases of gRIP. The solid improvements on the theoretical results are demonstrated and compared with the known results. Finally, we provide a series of simulations to verify the correctness of the theoretical assertions as well as the effectiveness of the AIT algorithm.
No keywords uploaded!
[ Download ] [ 2017-01-26 17:34:15 uploaded by JinshanZeng ] [ 625 downloads ] [ 0 comments ]
@inproceedings{yulinear,
  title={Linear convergence of adaptively iterative thresholding algorithms for compressed sensing},
  author={Yu Wang, Jinshan Zeng, Zhimin Peng, Xiangyu Chang, and Zongben Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170126173415482463127},
}
Yu Wang, Jinshan Zeng, Zhimin Peng, Xiangyu Chang, and Zongben Xu. Linear convergence of adaptively iterative thresholding algorithms for compressed sensing. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170126173415482463127.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved