固定时间梯度流在l1-l2范数中的稀疏重构

胡登洲; 何兴

doi:10.21656/1000-0887.400202

固定时间梯度流在l₁-l₂范数中的稀疏重构

doi: 10.21656/1000-0887.400202

胡登洲,
何兴

西南大学电子信息工程学院, 重庆 400700

基金项目: 国家自然科学基金(61773320)

详细信息

作者简介:
胡登洲(1992—)，男，硕士生(E-mail: 1076060236@qq.com)；何兴(1986—)，男，教授，博士生导师(通讯作者. E-mail: hexingdoc@swu.edu.cn).

中图分类号: O357.41
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- 被引次数: 0
出版历程
- 收稿日期: 2019-07-02
- 修回日期: 2019-07-09
- 刊出日期: 2019-11-01

Sparse Reconstruction of Fixed-Time Gradient Flow in the l₁-l₂ Norm

College of Electronic and Information Engineering, Southwest University, Chongqing 400700, P.R.China

Funds: The National Natural Science Foundation of China(61773320)

摘要

摘要: 压缩感知（compressed sensing，CS）是一种全新的信号采样技术，对于稀疏信号，它能够以远小于传统的Nyquist采样定理的采样点来重构信号。在压缩感知中，采用动态连续系统，对l₁-l₂范数的稀疏信号重构问题进行了研究。提出了一种基于固定时间梯度流的稀疏信号重构算法，证明了该算法在Lyapunov意义上的稳定性并且收敛于问题的最优解。最后通过与现有的投影神经网络算法的对比，体现了该算法的可行性以及在收敛速度上的优势.
- 压缩感知 /
- l₁-l₂范数 /
- 固定时间梯度流 /
- 稀疏信号重构
Abstract: The compressed sensing (CS) is a new signal sampling technology, which can reconstruct signals at sampling points far smaller than those in the traditional Nyquist sampling theorem for sparse signals. For the compressed sensing, a dynamic continuous system was used to study the sparse signal reconstruction of the l₁l-l₂ norm. A sparse signal reconstruction algorithm based on the fixed time gradient flow was proposed, and was proved to be stable in the sense of Lyapunov and to converge to the optimal solution of the problem. Finally, the feasibility and advantages in the convergence speed of this algorithm were demonstrated through comparison between the proposed algorithm and existing projection neural network algorithms.
- compressed sensing /
- l₁-l₂ norm /
- fixed-time gradient flow /
- sparse signal reconstruction

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参考文献(26)

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