脉冲噪声环境下基于洛伦兹范数软阈值迭代的压缩感知算法

观测值受脉冲噪声干扰情况下,传统的压缩感知算法基本失效,基于洛伦兹范数的硬阈值迭代(LIHT)算法是有效途径,但是硬阈值迭代过程会误判信号支撑集,随着脉冲数目增加,算法性能明显下降。针对这一问题,提出了一种基于洛伦兹范数的软阈值迭代(LIST)压缩感知重构算法。利用洛伦兹范数有效约束脉冲噪声,引入信号稀疏度度量函数,采用梯度下降法降低重构信号的稀疏度,实现软阈值迭代,并通过拟牛顿法求解该模型,加快算法收敛,运算量与其他算法是同一数量级,数值仿真表明,重构信噪比优于LIHT算法。     

基于Group lasso的分布式MIMO雷达参数估计与能量优化

针对压缩感知算法在分布式MIMO 雷达参数估计性能上易受噪声影响而出现伪峰、定位不准等问题,结合目标散射系数所满足块稀疏的前提条件,提出了一种基于Group lasso 模型框架下压缩感知算法的参数估计.Group lasso 作为一种块稀疏模型,可以有效解决感知算法在低SNR 时参数估计性能差的问题,有效抑制了噪声对稀疏信号的破坏,其性能明显优于感知算法中常用的凸松弛CVX 方法.此外针对MIMO雷达目标散射系数准确估计的前提,提出了基于线性规划的发射能量优化分配策略,此时系统模型转化为单发多收的MISO 雷达,且集中发射功率于散射系数较大的路径.仿真结果表明,优化发射能量后的MISO雷达性能优势明显,尤其是当路径起伏较大时,性能尤为突出.仿真实验验证了理论分析的正确性和算法模型的有效性.     

压缩感知理论与非凸优化方法研究

针对某些信号带宽较宽导致难以直接采样的问题,压缩感知理论提供了一种可行的低速采样方法。信号在特定变换域中拥有稀疏表示,通过低速采样得到少量的投影值,已经包含了重构所需的重要信息。利用压缩感知理论从投影值中重构出稀疏向量,进而重建原信号。同时介绍一种基于非凸优化的压缩感知重构算法。相比L1范数的凸优化和无稀疏约束的L2范数,非凸优化的Lp范数拥有对稀疏性更强的约束。实验结果表明,使用压缩感知理论可以显著降低对信号的采样速率,而使用非凸优化算法可以取得更好的重构效果。     

一种快速的压缩感知信号重构算法

重构算法是压缩感知技术的重要环节之一,文中针对现有重构算法收敛速度较慢的问题,提出了一种适用于压缩感知的快速重构算法。该方法的思想是在求解过程中,设计一种有效的步长迭代方案,以此来更新由梯度Lipschitz指数确定的迭代步长,再利用更新后的步长对原始信号的稀疏域表示向量进行迭代收缩,提高收敛速度。实验结果表明,相比传统的正交匹配追踪(OMP)算法、固定步长的l1范数重构算法,该方法在保证信号恢复精度的前提下,具有更快的收敛速度和更高的重构精度。     

一阶Born近似下的不均匀目标贝叶斯压缩感知微波成像方法

针对不均匀散射体重构问题,提出了一种基于Born 近似下的贝叶斯压缩感知微波成像方法。在一阶Born 近似框架下,基于电场积分方程并对成像区域网格离散建立稀疏感知模型,然后构造基于高斯先验的贝叶斯概率密度函数,并利用相关向量机方法对目标函数进行优化求解,最终实现对目标的微波成像。通过对多像素单目标、不均匀单目标、不均匀多目标等的微波成像研究并考虑了噪声影响,数值算例结果表明基于高斯先验的贝叶斯压缩感知方法重构结果要优于共轭梯度迭代算法和正交匹配追踪压缩感知重构算法,验证了文中方法的有效性和鲁棒性。     

基于SWCoSaMP算法的稀疏信号重构

压缩感知(compressed sensing,CS)稀疏信号重构本质上是在稀疏约束条件下求解欠定方程组。针对压缩感知匹配追踪(compressed sampling matching pursuit,CoSaMP)算法直接从代理信号中选取非零元素个数两倍作为支撑集,但是不存在迭代量化标准,本文提出了分步压缩感知匹配追踪(stepwise compressed sampling matchingpursuit,SWCoSaMP)算法。该算法从块矩阵的逆矩阵定义出发,采用迭代算法得到稀疏信号的支撑集,推出每次迭代支撑集所对应重构误差的L-2范数闭合表达式,从而重构稀疏信号。实验结果表明和原来CoSaMP算法相比,对于非零元素幅度服从均匀分布和高斯分布的稀疏信号,新算法具有更好的重构效果。     

基于稀疏脉冲反演的墙体参数研究

稀疏脉冲反演实际上是从含有噪声的雷达数据单道中计算出具有稀疏分布特性的反射系数。文中以范数约束为基础,提出L1 范数约束求解的方法,并且采用迭代重加权最小二乘法(IRLS)的优化算法,该算法具有精度高、速度快的优点,对穿墙侦查雷达数据处理后可以有效提高分辨率,获得反射系数,有助于进一步求得墙体的厚度和介电常数。最后针对不同数据的实验结果验证了算法的有效性。     

一种基于单像素相机的压缩感知图像重建优化算法

基于压缩感知图像重构和单像素相机成像的基本原理,对单像素成像系统中的图像重建算法进行了改进优化。基于最小范数类优化算法,结合凸优化算法和非凸优化算法各自的优点,设计了一种逼近L₀范数的数学模型,从而实现了从凸优化向非凸优化算法的迭代逼近,即逼近光滑L₀范数算法。该新型算法以更高的效率和更大的概率逼近原始信号全局最优且尽可能稀疏的解。相较于传统压缩感知图像重建的贪婪类算法和最小范数类算法,该算法使压缩感知重建图像的质量和单像素相机的成像效果均得到了有效提升,并通过实验仿真和实际场景的成像实验验证了该优化算法的可行性。     

基于Monte Carlo采样的压缩感知弱匹配去噪重构

最小二乘是现有贪婪迭代类压缩感知重构算法中通用的信号估计方法,其未考虑到可能将量测噪声引入信号估计的情况.针对以上不足,提出一种基于Monte Carlo采样的压缩感知弱匹配去噪重构算法.该算法在未知信号稀疏度先验的条件下,通过引入递推Bayesian估计减小量测噪声的干扰;同时,以弱匹配的方式筛选出有效的原子,并剔除冗余原子进而重构原信号.新算法继承了现有贪婪迭代类算法的有效性,同时避免了因噪声干扰或稀疏度未知导致的重构失败.理论分析和实验表明,新算法在同等条件,尤其是非高斯噪声情况下,重构性能优于现有典型贪婪迭代类算法,且其运算时间低于BPDN算法和同类的KF-SAMP算法.     

基于卡尔曼滤波的压缩感知弱匹配去噪重构

现有的贪婪迭代类压缩感知重构算法均基于最小二乘对信号进行波形估计,未考虑到可能将量测噪声引入信号估计的情况.针对以上不足,提出了一种基于线性Kalman滤波的压缩感知弱匹配去噪重构算法.该算法不需已知稀疏度先验,通过引入Kalman滤波,在最小均方误差准则下,每次迭代都获得最佳信号估计;并以弱匹配的方式同时筛选出有效的原子,并剔除冗余原子进而重构原信号.新算法继承了现有贪婪迭代类算法的有效性,同时避免了因噪声干扰或稀疏度未知导致的重构失败.理论分析和实验表明,新算法在同等条件下,重构性能优于现有典型贪婪迭代类算法,且其运算时间低于BPDN算法和同类的KFCS算法.     

含脉冲噪声的洛伦兹双阈值余量追踪信号重构

在压缩感知(CS)技术中,基于最小洛伦兹范数的重构算法在脉冲噪声环境下具有较强的鲁棒性。但是,洛伦兹硬阈值追踪(LHTP)算法采用残差的负梯度更新信号的估计量,从中引入了噪声的影响。基于此,提出了洛伦兹双阈值余量追踪(LDTRP)算法,通过迭代估计的重构误差来修正信号的估计量,并利用残差设置新的野点阈值。实验结果表明,无论信号是否受到噪声影响,LDTRP算法均能获得更好的信号重构质量。另外,在含有脉冲噪声的环境中,相比洛伦兹迭代硬阈值(LIHT)算法与LHTP算法,所提算法降低了对脉冲数量以及脉冲功率变化的敏感度,提高了重构性能。     

Novel method based on fractional lower-order correntropy-analogous statistics for parameter jointly estimation in bistatic MIMO radar

According to the performance degradation problem of parameter estimation algorithm in the Alpha stable dis-tribution noise, inspired by the concept of correntropy, a new class of statistics, namely, the fractional lower-order cor-rentropy-analogous statistics (FCAS) was proposed. By employing the fractional lower-order correntropy-analogous sta-tistics based cost function in parallel factor (PARAFAC), the FCAS-PARAFAC algorithm was deduced which can be utilized for the parallel factor under impulsive noise environments. The FCAS-PARAFAC algorithm was applied to pa-rameter estimation in bistatic MIMO radar under impulsive noise environment. The proposed method can suppress the impulse noise interference and has better estimation performance. Furthermore, the estimated parameters are automati-cally paired without the additional pairing method. Simulation results are presented to verify the effectiveness of the pro-posed method.     

基于稀疏信号重构的近场源定位

针对近场源定位问题,提出了一种基于稀疏信号重构的定位方法.该方法通过约束稀疏信号的L1-范数求解优化问题,实现信源的定位.该方法采用一种新的方法约束噪声项系数以求解优化问题,无需噪声的先验知识.为了减小计算量,将近场源二维定位问题转化为两次一维参数估计.通过计算机仿真验证了该方法的性能.     

Bayesian Sparse Reconstruction Method of Compressed Sensing in the Presence of Impulsive Noise

The majority of existing recovery algorithms in the framework of compressed sensing are not robust to the impulsive noise. However, the impulsive noise is always present in the actual communication and signal processing system. In this paper, we propose a method named ‘Bayesian sparse reconstruction’ to recover the sparse signal from the measurement vector which is corrupted by the impulsive noise. The Bayesian sparse reconstruction method is composed of five parts, which are the preliminary detection of the location set of impulses, the impulsive noise fast relevance vector machine algorithm, the step of pruning, Bayesian impulse detection algorithm and the maximum a posteriori estimate of the sparse vector. The Bayesian sparse reconstruction method can achieve effective signal recovery in the presence of impulsive noise, depending on the mutual influence of the impulsive noise fast relevance vector machine algorithm, the step of pruning and the Bayesian impulse detection algorithm. Experimental results show that the Bayesian sparse reconstruction method is robust to the impulsive noise and effective in the additive white Gaussian noise environment.     

基于稀疏贝叶斯学习的MIMO-OFDM电力线通信系统接收机设计

丰富的脉冲噪声干扰对基于MIMO-OFDM技术的电力线通信系统接收机设计带来了巨大挑战。针对这个问题,提出了一种联合估计电力线信道和脉冲噪声的接收机设计方案。该方案主要利用电力信道多径模型参数在频域上的稀疏性和脉冲噪声在时域上的稀疏性特征,将待估计信道模型参数和脉冲噪声联合视作一个稀疏向量,同时利用MIMO系统的空间相关性,构建了一个基于多测量向量的压缩感知模型,并引入多测量向量稀疏贝叶斯学习理论,设计了一种联合估计MIMO信道模型参数和脉冲噪声的方法。仿真结果表明,与传统的MIMO信道估计与脉冲噪声抑制相互分离的接收机方案相比,新方法在估计性能和误比特率性能上有明显提升。     

脉冲噪声环境下高斯稀疏信源贝叶斯压缩感知重构

 大多数现有的压缩感知重构算法对脉冲噪声不具有鲁棒性,在脉冲噪声环境下,重构性能急剧下降,使得整个重构系统崩溃.针对此问题,本文提出了一种脉冲噪声环境下的稀疏重构算法BINSR算法,其基于贝叶斯理论,可以有效地估计出信号的支撑集和脉冲噪声中脉冲的位置,并且根据压缩感知观测序列的democracy特性,利用最小均方误差MMSE估计量,有效地估计出原信号.在此基础上,本文结合鲁棒统计学,提出自适应的ABINSR算法,使其不再依赖于信号以及噪声的统计参数.实验结果表明,BINSR算法在脉冲噪声环境下可以有效地恢复出稀疏信号,很大程度上改善了脉冲噪声环境下算法的重构性能.ABINSR算法不仅对脉冲噪声具有鲁棒性,而且可以在高斯白噪声环境下实现有效的信号重构.     

System parameter estimation with input/output noisy data andmissing measurements

An investigation is undertaken to examine the parameter estimation problem of linear systems when some of the measurements are unavailable (i.e., missing data) and the probability of occurrence of missing data is unknown a priori. The system input and output data are also assumed to be corrupted by measurement noise, and the knowledge of the noise distribution is unknown. Under the unknown noise distribution and missing measurements, a consistent parameter estimation algorithm [which is based on an l_p norm iterative estimation algorithm-iteratively reweighted least squares (IRLS)] is proposed to estimate the system parameters. We show that if the probability of missing measurement is less than one half, the parameter estimates via the proposed estimation algorithm will converge to the true parameters as the number of data tends to infinity. Finally, several simulation results are presented to illustrate the performance of the proposed l _p norm iterative estimation algorithm. Simulation results indicate that under input/output missing data and noise environment, the proposed parameter estimation algorithm is an efficient approach toward the system parameter estimation problem     

Robust Symbol Rate Estimation of PSK Signals Under the Cyclostationary Framework

In many communication channels the noise is non-Gaussian and usually exhibits impulsive characteristics. The symbol rate estimation problem of phase-shift keying (PSK) signals in this kind of impulsive noise environment is addressed. Since the performance of the cyclic statistics-based symbol rate estimation methods, which are very effective in Gaussian noise, may deteriorate significantly in the presence of impulsive noise, a robust method under the cyclostationary framework is proposed. Specifically, a robust form of cyclic autocorrelation based on the M-estimate concept is developed. Simulation results show that the proposed robust technique offers a significant performance gain over the cyclic autocorrelation method in impulsive noise.     

Parameter estimation based on fractional power spectrum under alpha-stable distribution noise environment in wideband bistatic MIMO radar system

This paper takes the alpha-stable distribution as the noise model and works on the parameter estimation problem of wideband bistatic Multiple-Input Multiple-Output (MIMO) radar system in the impulsive noise environment. In many applications, it is not appropriate to approximate the wideband signal by the narrowband model. Furthermore, the echo signal may be corrupted by the non-Gaussian noise. The conventional algorithms degenerate severely in the impulsive noise environment. Thus, this paper proposes a new wideband signal model and a novel method in wideband bistatic MIMO radar system. It combines the fractional lower order statistics and fractional power spectrum, for suppressing the impulse noise and estimating parameters of the target. Firstly, a new signal array model is proposed under the alpha-stable distribution noise model. Secondly, Doppler stretch and time delay are jointly estimated by peak searching of the FLOS-FPSD. Furthermore, two modified algorithms are proposed for the estimation of the direction-of-departure and direction-of-arrival, including the fractional power spectrum density based on MUSIC algorithm (FLOS-FPSD-MUSIC) and the fractional lower-order ambiguity function based on ESPRIT algorithm (FLOS-FPSD-ESPRIT). Simulation results are presented to verity the effectiveness of the proposed method.     

一种改进的广义循环相关熵时延估计方法

针对同频带干扰及脉冲噪声并存的复杂电磁环境下现有时延估计算法性能退化的问题,该文引入双曲正切函数,提出一种改进的广义循环相关熵时延估计(HTGCCE)算法。首先指出脉冲噪声存在时广义循环相关熵算法的优势及性能退化的原因。然后利用双曲正切函数对其进行改进,以提高算法在脉冲噪声下的时延估计性能。仿真实验表明,提出的算法在脉冲噪声的特征指数较小、信噪比较低及信干比较低时仍保持很好的时延估计性能。