Recovery of signals under the condition on RIC and ROC via prior support information

In this paper, the sufficient condition in terms of the RIC and ROC for the stable and robust recovery of signals in both noiseless and noisy settings was established via weighted $l_1$ minimization when there is partial prior information on support of signals. An improved performance guarantee has been derived. We can obtain a less restricted sufficient condition for signal reconstruction and a tighter recovery error bound under some conditions via weighted $l_1$ minimization. When prior support estimate is at least 50% accurate, the sufficient condition is weaker than the analogous condition by standard $l_1$ minimization method, meanwhile the reconstruction error upper bound is provably to be smaller under additional conditions. Furthermore, the sufficient condition is also proved sharp.     

CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix–vector multiplies with the sampling matrix. For compressible signals, the running time is just O(Nlog²N), where N is the length of the signal.     

Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L₁-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L₁-minimization. Our algorithm, ROMP, reconstructs a sparse signal in a number of iterations linear in the sparsity, and the reconstruction is exact provided the linear measurements satisfy the uniform uncertainty principle.      

Convergence of projected Landweber iteration for matrix rank minimization

In this paper, we study the performance of the projected Landweber iteration (PLW) for the general low rank matrix recovery. The PLW was first proposed by Zhang and Chen (2010) [43] based on the sparse recovery algorithm APG (Daubechies et al., 2008) [14] in the matrix completion setting, and numerical experiments have been given to show its efficiency (Zhang and Chen, 2010) [43]. In this paper, we focus on providing a convergence rate analysis of the PLW in the general setting of low rank matrix recovery with the affine transform having the matrix restricted isometry property. We show robustness of the algorithm to noise with a strong geometric convergence rate even for noisy measurements provided that the affine transform satisfies a matrix restricted isometry property condition.     

Analysis of orthogonal multi-matching pursuit under restricted isometry property

Orthogonal multi-matching pursuit(OMMP)is a natural extension of orthogonal matching pursuit(OMP)in the sense that N(N≥1)indices are selected per iteration instead of 1.In this paper,the theoretical performance of OMMP under the restricted isometry property(RIP)is presented.We demonstrate that OMMP can exactly recover any K-sparse signal from fewer observations y=φx,provided that the sampling matrixφsatisfiesδKN-N+1+(K/N)~(1/2)θKN-N+1,N1.Moreover,the performance of OMMP for support recovery from noisy observations is also discussed.It is shown that,for l_2 bounded and l_∞bounded noisy cases,OMMP can recover the true support of any K-sparse signal under conditions on the restricted isometry property of the sampling matrixφand the minimum magnitude of the nonzero components of the signal.     

弱化限制等距性的稀疏信号恢复

众所周知,传统的信号压缩和重建遵循香农一耐奎斯特采样定律,即采样率必须至少为信号最高频率的两倍,才能保证在重建时不产生失真,这无疑将给信号采样,传输和存储过程带来越来越大的压力.随着科技的飞速发展,特别是近年来传感器技术获取数据能力提高,物联网等促使人类社会的数据规模遽增,大数据时代正式到来.大数据的规模效应给数据存储,传输,管理以及数据分析带来了极大的挑战.压缩采样应运而生.限制等距性(Restricted Isometry Property,RIP)在压缩传感中起着关键的作用.只有满足限制等距条件的压缩矩阵才能平稳恢复原始信号.RIP作为衡量矩阵是否能作为测量矩阵得到了认可,但是此理论的缺陷在于对任一矩阵,很难有通用,快速的算法来验证其是否满足RIP条件.很多学者尝试弱化RIP条件以找到测量矩阵构造的突破口.首先构造了新的限制等距条件δ_(1.5k)+θ_(k,1.5k)≤1,然后证明在这个条件下无噪声稀疏信号能被精确的恢复,并且噪声稀疏信号能被平稳的估计.最后,通过比较表明δ_(1.5k)+θ_(k,1.5k)≤1优于现存的条件.     

矩阵方程ATXB+BTXTA=D的极小范数最小二乘解

1引言本文用Rm×n表示所有m×n实矩阵全体,ORn×n,ASRn×n分别表示n×n实正交矩阵类与反对称矩阵类.‖·‖F表示矩阵的Frobenius范数,A+为矩阵A的Moore-Penrose广义逆,A*B与A(?)B分别表示矩阵4与B的Hadamard乘积及Kronecker乘积,即若A=(aij),B=(bij),则A*B=(ajibij),A(?)B=(aijB),vec4表示矩阵A的按行拉直,即若A=[aT1,aT2,…,aTm],其中ai为A的行向量,则vecA=(a1a2…am)T.设A∈Rn×m,B∈Rp×m,D∈Rm×m,我们考虑不相容线性矩阵方程ATXB+BTXTA=D(1.1)     

矩阵方程ATXA=C的双对称最小二乘解的最佳逼近

1引言根据矩阵分解理论求解线性矩阵方程的问题已经有多位作者研究([2],[3],[5]-[11]),比如文[6],[7],[9]基于GSVD、CCD方法给出了几个矩阵方程的最小二乘解以及方程(组)相     

基于Chebyshev多项式的神经网络中长期负荷预测研究

高精度负荷预测在提高电力系统的安全性和经济性方面有着极其重要的意义,而现有的负荷预测方法因参数有限,难以完全反映其内在规律,因而导致预测结果不够准确.为此提出了一种基于Chebyshev多项式神经网络模型的预测方法.该方法使用递推最小二乘法训练神经网络权值系数,以获得高精度的参数估计,从而实现Chebyshev多项式神经网络模型对负荷量的最优拟合,再利用训练好的Chebyshev多项式神经网络模型实现中长期负荷预测.研究结果表明,该方法能较好模拟负荷变化规律,有效提高了负荷预测精度,在电力系统负荷预测中有较大的应用价值.     

Asymptotic properties of the least squares estimators of the parameters of the chirp signals

Chirp signals are quite common in different areas of science and engineering. In this paper we consider the asymptotic properties of the least squares estimators of the parameters of the chirp signals. We obtain the consistency property of the least squares estimators and also obtain the asymptotic distribution under the assumptions that the errors are independent and identically distributed. We also consider the generalized chirp signals and obtain the asymptotic properties of the least squares estimators of the unknown parameters. Finally we perform some simulations experiments to see how the asymptotic results behave for small sample and the performances are quite satisfactory.     

半定矩阵秩极小的非凸精确松弛

本文主要研究半定矩阵秩极小问题(P)的非凸精确松弛及其性质.首先,为求解问题(P),我们引入其Schatten p-范数(0＜p＜1)松弛,记为(Sp).其次,通过定义半定限制等距常数和半定限制正交常数,我们给出了问题(P)有唯—解的充分条件.最后,利用半定限制等距性质,我们给出了问题(P)和(Sp)有相同唯一解的充分条件.特别地,对任意0＜p＜1,我们还得到—个一致的精确恢复条件.     

Weighted $\ell_p$-Minimization for Sparse Signal Recovery under Arbitrary Support Prior

Weighted $\ell_p$ ($0相似文献