A Perturbation Analysis on Compressed Data Separation with Nonconvex Minimization Method

LIU Chun-yan; WANG Jian-jun; WANG Wen-dong; WANG Yao

doi:10.3969/j.issn.0372-2112.2017.01.006

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A Perturbation Analysis on Compressed Data Separation with Nonconvex Minimization Method

更新时间：2025-07-16

- A Perturbation Analysis on Compressed Data Separation with Nonconvex Minimization Method
- Acta Electronica Sinica Vol. 45, Issue 1, Pages: 37-45(2017)
- 作者机构：
  
  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
  5. 西南大学数学与统计学院,重庆,400715
  6. 西南大学计算机与信息科学学院,重庆,400715
  7. 西安交通大学数学与统计学院,陕西,西安,710049
  8. 重庆师范大学涉外商贸学院数学与计算机学院,重庆,400715
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61273020, No.11001227, No.61673015);Fundamental Research Funds for the Central Universities (No.XDJK2015A007)
- DOI：10.3969/j.issn.0372-2112.2017.01.006
  CLC： TN911.72
- Published Online：25 January 2017，
  
  Published：2017
- 稿件说明：
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LIU Chun-yan, WANG Jian-jun, WANG Wen-dong, et al. A Perturbation Analysis on Compressed Data Separation with Nonconvex Minimization Method[J]. Acta Electronica Sinica, 2017, 45(1): 37-45.
DOI：

LIU Chun-yan, WANG Jian-jun, WANG Wen-dong, et al. A Perturbation Analysis on Compressed Data Separation with Nonconvex Minimization Method[J]. Acta Electronica Sinica, 2017, 45(1): 37-45. DOI： 10.3969/j.issn.0372-2112.2017.01.006.

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l

（0

1）极小化的压缩数据分离问题的重构条件和误差估计，理论结果表明在不同冗余字典和不同扰动下，此方法仍能鲁棒重构原始信号.基于两种不同的冗余字典-离散余弦变换（DCT）和小波变换（WT），我们执行了一系列仿真实验，验证了在测量矩阵受各种扰动和加性噪音下，非凸l

（0

1）极小化方法具有较强的鲁棒性和稳定性.本文结果为压缩感知和数据分离的进一步发展和应用提供借鉴.

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 l

1) minimization are established.Under different redundant dictionaries and perturbation

our results show that nonconvex l

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 sim

ulation experiments to testify the strong robustness and stability of nonconvex l

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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