The performance guarantees of generalized orthogonal matching pursuit（ gOMP） are considered in the framework of mutual coherence. The gOMP algorithmis an extension of the well-known OMP greed algorithmfor compressed...The performance guarantees of generalized orthogonal matching pursuit（ gOMP） are considered in the framework of mutual coherence. The gOMP algorithmis an extension of the well-known OMP greed algorithmfor compressed sensing. It identifies multiple N indices per iteration to reconstruct sparse signals.The gOMP with N≥2 can perfectly reconstruct any K-sparse signals frommeasurement y = Φx if K 〈1/N（1/μ-1） ＋1,where μ is coherence parameter of measurement matrix Φ. Furthermore,the performance of the gOMP in the case of y = Φx ＋ e with bounded noise ‖e‖2≤ε is analyzed and the sufficient condition ensuring identification of correct indices of sparse signals via the gOMP is derived,i. e.,K 〈1/N（1/μ-1）＋1-（2ε/Nμxmin） ,where x min denotes the minimummagnitude of the nonzero elements of x. Similarly,the sufficient condition in the case of G aussian noise is also given.展开更多
The conventional two dimensional(2D)inverse synthetic aperture radar(ISAR)imaging fails to provide the targets'three dimensional(3D)information.In this paper,a 3D ISAR imaging method for the space target is propos...The conventional two dimensional(2D)inverse synthetic aperture radar(ISAR)imaging fails to provide the targets'three dimensional(3D)information.In this paper,a 3D ISAR imaging method for the space target is proposed based on mutliorbit observation data and an improved orthogonal matching pursuit(OMP)algorithm.Firstly,the 3D scattered field data is converted into a set of 2D matrix by stacking slices of the 3D data along the elevation direction dimension.Then,an improved OMP algorithm is applied to recover the space target's amplitude information via the 2D matrix data.Finally,scattering centers can be reconstructed with specific three dimensional locations.Numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed 3D imaging method.展开更多
针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法...针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法。AQ-ADMM算法在经典交替方向乘子算法算法迭代过程中添加二次临近项,且能够自适应选取惩罚参数。首先在数据中心建立信号参考数据库用于构造初始字典,然后将K-奇异值分解(K-singular value decomposition, K-SVD)字典学习算法和AQ-ADMM算法结合重构缺失信号。对仿真信号和两种真实轴承信号数据集添加高斯白噪声后作为样本,试验结果表明当信号压缩率在50%~70%时,所提方法性能指标明显优于其它传统方法,在重构信号的同时实现了对含缺失数据机械振动信号的快速精确修复。展开更多
提出一种压缩感知正交匹配追踪（CS-OMP）超谐波测量新算法,即运用压缩感知理论,通过引入插值系数,基于离散傅里叶变换（DFT）系数向量和狄利克雷核矩阵,构建了高频率分辨率的压缩感知模型,并基于正交匹配追踪算法,在不增加被测数据观...提出一种压缩感知正交匹配追踪（CS-OMP）超谐波测量新算法,即运用压缩感知理论,通过引入插值系数,基于离散傅里叶变换（DFT）系数向量和狄利克雷核矩阵,构建了高频率分辨率的压缩感知模型,并基于正交匹配追踪算法,在不增加被测数据观测时间前提下,将超谐波测量的频率分辨率提高了一个数量级。数值仿真分析以及两种非线性负荷的实测数据验证的结果表明,该算法可将测得数据频率分辨率由2 k Hz细化为200 Hz,能实现对被测信号中超谐波频率成分的精确定位,也可准确求解出其幅值信息,从而有效地弥补了DFT算法存在的观测时间与频率分辨率互相限制的固有缺陷,在更准确测量超谐波方面展现出良好前景。展开更多
基金Supported by the National Natural Science Foundation of China(60119944,61331021)the National Key Basic Research Program Founded by MOST(2010C B731902)+1 种基金the Program for Changjiang Scholars and Innovative Research Team in University(IRT1005)Beijing Higher Education Young Elite Teacher Project(YET P1159)
文摘The performance guarantees of generalized orthogonal matching pursuit（ gOMP） are considered in the framework of mutual coherence. The gOMP algorithmis an extension of the well-known OMP greed algorithmfor compressed sensing. It identifies multiple N indices per iteration to reconstruct sparse signals.The gOMP with N≥2 can perfectly reconstruct any K-sparse signals frommeasurement y = Φx if K 〈1/N（1/μ-1） ＋1,where μ is coherence parameter of measurement matrix Φ. Furthermore,the performance of the gOMP in the case of y = Φx ＋ e with bounded noise ‖e‖2≤ε is analyzed and the sufficient condition ensuring identification of correct indices of sparse signals via the gOMP is derived,i. e.,K 〈1/N（1/μ-1）＋1-（2ε/Nμxmin） ,where x min denotes the minimummagnitude of the nonzero elements of x. Similarly,the sufficient condition in the case of G aussian noise is also given.
文摘The conventional two dimensional(2D)inverse synthetic aperture radar(ISAR)imaging fails to provide the targets'three dimensional(3D)information.In this paper,a 3D ISAR imaging method for the space target is proposed based on mutliorbit observation data and an improved orthogonal matching pursuit(OMP)algorithm.Firstly,the 3D scattered field data is converted into a set of 2D matrix by stacking slices of the 3D data along the elevation direction dimension.Then,an improved OMP algorithm is applied to recover the space target's amplitude information via the 2D matrix data.Finally,scattering centers can be reconstructed with specific three dimensional locations.Numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed 3D imaging method.
文摘针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法。AQ-ADMM算法在经典交替方向乘子算法算法迭代过程中添加二次临近项,且能够自适应选取惩罚参数。首先在数据中心建立信号参考数据库用于构造初始字典,然后将K-奇异值分解(K-singular value decomposition, K-SVD)字典学习算法和AQ-ADMM算法结合重构缺失信号。对仿真信号和两种真实轴承信号数据集添加高斯白噪声后作为样本,试验结果表明当信号压缩率在50%~70%时,所提方法性能指标明显优于其它传统方法,在重构信号的同时实现了对含缺失数据机械振动信号的快速精确修复。
文摘提出一种压缩感知正交匹配追踪（CS-OMP）超谐波测量新算法,即运用压缩感知理论,通过引入插值系数,基于离散傅里叶变换（DFT）系数向量和狄利克雷核矩阵,构建了高频率分辨率的压缩感知模型,并基于正交匹配追踪算法,在不增加被测数据观测时间前提下,将超谐波测量的频率分辨率提高了一个数量级。数值仿真分析以及两种非线性负荷的实测数据验证的结果表明,该算法可将测得数据频率分辨率由2 k Hz细化为200 Hz,能实现对被测信号中超谐波频率成分的精确定位,也可准确求解出其幅值信息,从而有效地弥补了DFT算法存在的观测时间与频率分辨率互相限制的固有缺陷,在更准确测量超谐波方面展现出良好前景。
