Symmetric Toeplitz-Structured Compressed Sensing Matrices

被引：6
作者：
Huang T. [1 ,2 ]
Fan Y.-Z. [1 ,2 ]
Zhu M. [1 ,2 ]
机构：
[1] Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Anhui University, Hefei
[2] School of Mathematical Sciences, Anhui University, Hefei
来源：
Sensing and Imaging | 2015年 / 16卷 / 1期
基金：
中国国家自然科学基金; 高等学校博士学科点专项科研基金;
关键词：
Compressed sensing; Measurement matrix; Restricted isometry property; Symmetric Toeplitz-structured matrix;
D O I：
10.1007/s11220-015-0109-0
中图分类号：
学科分类号：
摘要：
How to construct a suitable measurement matrix is an important topic in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit some considerable structures. In this paper, we proved that a symmetric Toeplitz matrix and its variant can be used as measurement matrices and recovery signal with high probability. Compared with random matrices (e.g. Gaussian and Bernoulli matrices) and some structured matrices (e.g. Toeplitz and circulant matrices), we need to generate fewer independent entries to obtain the measurement matrix while the effectiveness of the recovery keeps good. © 2015, Springer Science+Business Media New York.
引用
收藏
页码：1 / 9
页数：8
相关论文
共 21 条
  • [1] Baraniuk R., Davenport M., DeVore R., Wakin M., A simple proof of the restricted isometry property for random matrices, Constructive Approximation, 28, 3, pp. 253-263, (2008)
  • [2] Candes E.J., The restricted isometry property and its implication for compressed sensing, Comptes Rendus Mathematique, 346, 9, pp. 589-592, (2008)
  • [3] Candes E., Romberg J., Tao T., Robust uncertainty principles: Exact signal recostruction from highly incomplete Fourier information, IEEE Transactions on Information Theory, 52, 2, pp. 489-509, (2006)
  • [4] Candes E.J., Tao T., Near optimal signal recovery from random projections: Universal encoding strategies, IEEE Transactions on Information Theory, 52, 12, pp. 5406-5425, (2006)
  • [5] Candes E.J., Tao T., Decoding by linear programming, IEEE Transactions on Information Theory, 51, pp. 4203-4215, (2005)
  • [6] Donoho D.L., Compressed sensing, IEEE Transactions on Information Theory, 52, 4, pp. 1289-1306, (2006)
  • [7] Fan Y.-Z., Huang T., Zhu M., Compressed sensing based on random symmetric Bernoulli matrix, arXiv, 1212, (2012)
  • [8] Fan Y.-Z., Huang T., Zhu M., Mixed compressed sensing based on random graphs, arXiv, 1307, (2013)
  • [9] Hajnal A., Szemeredi E., Proof of a conjecture of P Erdös, Combinatorial theory and its application, pp. 601-623, (1970)
  • [10] Haykin S., Adaptive filter theory, (2001)
123