| 基于非凸极小化的扰动压缩数据分离 |
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| 引用本文： | 刘春燕,王建军,王文东,王尧.基于非凸极小化的扰动压缩数据分离[J].电子学报,2017,45(1):37-45. |
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| 作者姓名： | 刘春燕 王建军 王文东 王尧 |
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| 作者单位： | 1. 西南大学数学与统计学院, 重庆 400715;
2. 西南大学计算机与信息科学学院, 重庆 400715;
3. 西安交通大学数学与统计学院, 陕西西安 710049;
4. 重庆师范大学涉外商贸学院数学与计算机学院, 重庆 400715 |
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| 基金项目： | 国家自然科学基金(61273020;61673015)，中央高校基本业务费项目(XDJK2015A007) |
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| 摘 要： | 压缩数据分离是信号采样理论的研究热点之一.本文给出了在冗余字典满足相互一致性条件和完全扰动矩阵满足限制性同构条件下，非凸lq（0q（0
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| 关 键 词： | 压缩数据分离 lq极小化 相互一致性 限制性等容性质 紧框架 完全扰动 |
| 收稿时间： | 2015-01-07 |
A Perturbation Analysis on Compressed Data Separation with Nonconvex Minimization Method |
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| LIU Chun-yan,WANG Jian-jun,WANG Wen-dong,WANG Yao.A Perturbation Analysis on Compressed Data Separation with Nonconvex Minimization Method[J].Acta Electronica Sinica,2017,45(1):37-45. |
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| Authors: | LIU Chun-yan WANG Jian-jun WANG Wen-dong WANG Yao |
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| Affiliation: | 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
2. School of Computer and Information Science, Southwest University, Chongqing 400715, China;
3. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China;
4. School of Mathematics and Computer, Chongqing Normal University Foreign Trade and Business College, Chongqing 400715, China |
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| Abstract: | Compressed data separation is one of the hot research theories of signal sampling.Under the condition that the redundant dictionary and perturbation matrix satisfy mutual coherence and restricted isometry property,respectively,the reconstruction condition and error estimation of compressed data separation via nonconvex lq (0 ＜ q ≤ 1) minimization are established.Under different redundant dictionaries and perturbation,our results show that nonconvex lq (0 ＜ q ≤ 1) minimization can still robustly reconstruct the original signal.In view of two different redundant dictionaries-the discrete cosine transform and wavelet transform,we conduct a series of simulation experiments to testify the strong robustness and stability of nonconvex lq (0 ＜ q ≤ 1) minimization method with various perturbation and additive noise.The obtained results provide a reference for further development and application of compressed sensing and data separation. |
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| Keywords: | compressed data separation lq minimization mutual coherence restricted isometry property (RIP) tight frames perturbation |
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