非合作跳频信号参数的盲压缩感知估计

针对非合作跳频通信系统采样速率高,先验信息少等问题,论文提出基于盲压缩感知重构理论参数估计算法。利用稀疏编码与正交基变换交替迭代的思想实现信号精确重构,并根据重构结果直接对跳频信号进行参数估计。与传统的压缩感知理论相比,盲压缩感知理论避免了对信号先验信息的需求,有效解决了非合作通信系统中先验信息少的问题。首先,建立信号模型,然后利用正交块对角盲压缩感知算法（Orthonormal Block Diagonal Blind Compressed Sensing,OBD-BCS）实现信号的重构,并估算出跳变频率及跳变周期。通过实验分析,该方法可以在低信噪比环境下恢复信号原始结构及信息,完成参数估计。      

基于迭代重赋权最小二乘算法的块稀疏压缩感知

压缩感知是一种新颖的信号处理理论。它突破了传统香农采样理论对采样的限制,以信号的稀疏性或可压缩性为基础,实现了信号的高效获取和精确重构。然而在现实中,部分稀疏信号还表现出一些其他结构,典型的例子就是一类块稀疏信号,其非零元素以块的形式出现。针对这类信号,本文研究了求解块稀疏压缩感知的迭代重赋权最小二乘算法（IRLS ）,给出了该算法的理论分析：误差估计和局部收敛性分析。大量试验验证了基于迭代重赋权最小二乘算法的块稀疏压缩感知策略的有效性。     

基于压缩感知的线性调频信号频率估计

基于压缩感知理论,测量了在不重构情况下线性调频信号的频率。算法根据信号的稀疏表示建立原子库,利用AIC(Analog-to-Information Conversion)技术完成对信号的压缩采样,在压缩域利用正交匹配追踪的算法进而优化重构稀疏系数,寻找出系数最大值所在的位置,而原子库中该位置原子的频率参量即为线性调频信号的频率参量。该方法在保证频率估计高成功率的前提下,大大减少了采样过程中的冗余和浪费,节省了存储空间,实验仿真验证表明该方法的可行性。     

基于块稀疏贝叶斯学习的雷达目标压缩感知(英文)

高速采样和传输是目前雷达系统面临的一个重要挑战。针对这一问题,该文提出一种利用信号块结构特性的雷达目标压缩感知方法。该方法采用一个简单的测量矩阵对信号进行采样,然后运用块稀疏贝叶斯学习算法恢复信号。经典的块稀疏贝叶斯学习算法适用于实信号,该文将其扩为可直接处理雷达信号的复数域稀疏贝叶斯算法。相对于现有压缩感知方法,该方法不仅具有更好的信号重构精度和鲁棒性,更重要的是其压缩测量矩阵形式简单、易于硬件实现。数值仿真实验结果验证了该方法的有效性。      

一种新型的扩频测控信号压缩采样结构

压缩感知理论能解决航天测控领域中扩频信号高带宽引发的采样压力和数据量过大的问题,压缩采样是压缩感知理论的主要应用之一,为降低前端信号采样压力和后端信号处理压力提供了一种新的途径。针对航天测控领域中最常见的直接序列扩频信号的压缩采样技术展开研究,提出了分段并行式随机重叠采样结构,并推导出采样结构的测量矩阵,结合信号的稀疏基利用匹配追踪算法对采样值进行重构。仿真实验表明,提出的采样结构能很好地适应高带宽扩频测控信号的压缩采样,能以较高的概率从低速的压缩采样值中恢复出原信号,相较于其他压缩采样结构在重构率、计算复杂度及稳定性方面具有较为显著的优势。     

动态稀疏频谱的自适应压缩感知与跟踪算法研究

在宽带频谱感知、通信侦察等应用中信号稀疏度往往是动态变化的。首先证明了重构误差随压缩比的增加单调减小,在此基础上,提出了一种压缩比随频谱稀疏度自适应调整的压缩采样新算法。新算法由压缩采样与压缩比自适应调整两部分组成,其中,压缩采样部分用于恢复原信号,并估计恢复信号与原信号之间的误差;压缩比自适应部分根据误差与压缩比之间的近似线性函数关系,自适应调整下一时刻的压缩比。计算机仿真结果表明:新算法能够以近似“最优”的压缩比对稀疏度慢变的频谱进行有效感知,并跟踪频谱稀疏度的变化;与传统压缩采样方法相比,在保证频谱感知精度的前提下,新算法能够总体上进一步显著降低采样速率。      

基于块稀疏度与自适应迭代的压缩感知方法

针对分块压缩感知算法在平滑块效应时损失了大量的细节纹理信息,从而影响图像的重构效果问题,提出了一种基于块稀疏信号的压缩感知重构算法。该算法先采用块稀疏度估计对信号的稀疏性做初步估计,通过对块稀疏度进行估算初始化阶段长,运用块矩阵与残差信号最匹配原则来选取支撑块,再运用自适应迭代计算实现对块稀疏信号的重构,较好地解决了浪费存储资源和计算量大的问题。实验结果表明,相比常用压缩感知方法,所提算法能明显减少运算时间,且能有效提高图像重构效果。     

基于压缩感知观测序列倒谱距离的语音端点检测算法

本文基于语音信号在离散余弦基上的近似稀疏性,采用稀疏随机观测矩阵和线性规划重构算法对语音信号进行压缩感知与重构。研究了语音信号的压缩感知观测序列特性,根据语音帧和非语音帧压缩感知观测序列频谱幅度分布分散且差异较大的特性,提出基于压缩感知观测序列倒谱距离的语音端点检测算法,并对4dB-20dB下的带噪语音进行端点检测仿真实验。仿真结果显示,基于压缩感知观测序列倒谱距离的语音端点检测算法与奈奎斯特采样下语音的倒谱距离端点检测算法一样具有良好的抗噪性能,但由于采用压缩采样,减少了端点检测算法的运算数据量。      

基于压缩感知的模拟到信息转换研究

压缩感知理论突破了Nyquist采样定理的约束,提出对稀疏信号可以以远低于Nyquist采样速率进行采样,并可以通过重构算法恢复出原信号。研究了基于压缩感知的模拟到信息转换系统,该系统由调制、低通滤波器和低速率采样3个模块组成,实现高频信号的低速率采样,并通过重构算法得到原信号。对模拟到信息转换系统的结构和原理进行了详细介绍,并应用Matlab对系统进行了大量的仿真分析,该系统能稳健地从较少的采样数据中恢复原信号。     

采用正交多项匹配的块稀疏信号重构算法

压缩感知,通过测量矩阵将原始信号从高维空间投影到低维空间,然后求解优化问题,从少量投影中重构出原始信号,是一种有效的信号采集技术。块稀疏信号是具有特殊结构的稀疏信号,其非零值是成块出现的。针对该信号的特点,提出一种采用正交多项匹配的块稀疏信号重构算法。该算法每次迭代选择多个最大相关子块,然后更新块索引集,以及迭代余量,最后求广义逆运算重构出原始信号。仿真结果表明,相比于大多数的现有算法,本文算法重构概率较高,运行时间较短,复杂度较低。      

基于稀疏贝叶斯学习的多频带雷达信号融合

针对多频带雷达信号融合,建立了多频带雷达信号表示模型,将多频带信号融合问题等价于一个信号表示问题。研究了基追踪算法在多频带信号融合中的局限性,研究表明:由于多个频带的稀疏分布,破坏了字典的相干性,使得基追踪算法可能无法收敛到真实的稀疏解。提出了基于稀疏贝叶斯学习的多频带信号融合方法,并证明了字典满足唯一表示性条件从而可以保证算法收敛到真实的稀疏解。实验表明:基于稀疏贝叶斯学习的多频带信号融合方法能够更加真实地反映目标散射特性。     

基于几何绕射模型的多频带信号融合新方法

多频带雷达信号融合处理利用从不同频段获取的目标在一维谱域呈稀疏分布的雷达观测数据,通过信号级相干融合来提高目标散射中心参数估计精度和一维距离像的分辨能力。传统谱估计类融合方法的性能都受限于模型阶数估计。而多频带的稀疏分布,破坏了观测系统矩阵的互相干性度量,从而使得基追踪（基于l1范数的稀疏表示）方法的全局最优解可能并不等于信号的真实稀疏表示。本文在GTD散射模型的基础上,提出了一种基于稀疏贝叶斯学习的融合方法,既避免了阶数估计,又克服了基追踪方法的缺陷。实验结果也表明了此方法的优越性。      

宽带协方差矩阵的多字典联合稀疏表示DOA估计

为了直接处理相干宽带信号和提高其波达方向估计的分辨率,提出一种基于宽带协方差矩阵的多字典联合稀疏分解估计方法。首先,利用多个频率点处的过完备基对其协方差矩阵进行稀疏表示,然后形成多个字典的多测量矢量稀疏表示模型,最后通过多字典稀疏表示系数的联合稀疏约束以求解稀疏反问题的形式实现宽带信号的波达方向估计。对于均匀线阵结构,多字典协方差矩阵稀疏表示系数的联合稀疏性使其不再受空域采样条件的限制,既可通过增大阵元间距提高分辨率,而又无空域混叠现象。通过对噪声功率的预估计抑制噪声,提高了波达方向估计的稳健性。另外,该方法与信号协方差矩阵的秩无关,对相干信号和不相干信号都适用。仿真实验验证了该方法的有效性。      

$rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation

In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method—the$ K$-SVD algorithm—generalizing the$ K$-means clustering process.$ K$-SVD is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence. The$ K$-SVD algorithm is flexible and can work with any pursuit method (e.g., basis pursuit, FOCUSS, or matching pursuit). We analyze this algorithm and demonstrate its results both on synthetic tests and in applications on real image data.     

基于联合稀疏谱重构的PPG信号降噪算法

针对光电容积脉搏波（Photoplethysmography,PPG）传感器数据采集降噪问题,本文提出一种基于联合稀疏重构的PPG信号运动噪声降噪算法.该算法通过构建同时间段内PPG信号和加速度信号的频谱矩阵,提取频谱矩阵稀疏特征和该矩阵行稀疏特征,利用压缩感知方法,将PPG信号运动噪声去除过程建模为联合稀疏信号重构过程,并将该过程进一步建模为最优化模型,通过迭代寻优来获得该模型的最优解,结合谱减法,从而有效去除PPG信号中的运动噪声,降低噪声对PPG信号的影响.仿真分析表明,本文提出的算法能有效去除PPG信号中的运动噪声,获得较好的降噪效果.     

块稀疏贝叶斯模型下的跳频信号时频分析

针对传统时频分析方法存在的时频聚集性差以及交叉项干扰的问题,本文将接收到的跳频信号进行分割,构建时频稀疏模型,利用模型中的统计特性和结构特性采用块稀疏贝叶斯学习算法对跳频信号的时频图进行重构,在不需知道稀疏度和噪声强度的情况下,得到了高精度的时频图。但是由于算法在高维参数空间进行参数估计时复杂度较高,本文采用近似替换的方法对该算法进行改进,将高维参数空间转换到原始参数空间计算,大大减少了算法的复杂度,仿真结果表明改进算法在低信噪比的情况下能有效的得到跳频信号的高精度时频图且复杂度大大降低。      

Compressed Sensing of Analog Signals in Shift-Invariant Spaces

A traditional assumption underlying most data converters is that the signal should be sampled at a rate exceeding twice the highest frequency. This statement is based on a worst-case scenario in which the signal occupies the entire available bandwidth. In practice, many signals are sparse so that only part of the bandwidth is used. In this paper, we develop methods for low-rate sampling of continuous-time sparse signals in shift-invariant (SI) spaces, generated by m kernels with period T . We model sparsity by treating the case in which only k out of the m generators are active, however, we do not know which k are chosen. We show how to sample such signals at a rate much lower than m/T, which is the minimal sampling rate without exploiting sparsity. Our approach combines ideas from analog sampling in a subspace with a recently developed block diagram that converts an infinite set of sparse equations to a finite counterpart. Using these two components we formulate our problem within the framework of finite compressed sensing (CS) and then rely on algorithms developed in that context. The distinguishing feature of our results is that in contrast to standard CS, which treats finite-length vectors, we consider sampling of analog signals for which no underlying finite-dimensional model exists. The proposed framework allows to extend much of the recent literature on CS to the analog domain.     

Exploiting Structure in Wavelet-Based Bayesian Compressive Sensing

Bayesian compressive sensing (CS) is considered for signals and images that are sparse in a wavelet basis. The statistical structure of the wavelet coefficients is exploited explicitly in the proposed model, and, therefore, this framework goes beyond simply assuming that the data are compressible in a wavelet basis. The structure exploited within the wavelet coefficients is consistent with that used in wavelet-based compression algorithms. A hierarchical Bayesian model is constituted, with efficient inference via Markov chain Monte Carlo (MCMC) sampling. The algorithm is fully developed and demonstrated using several natural images, with performance comparisons to many state-of-the-art compressive-sensing inversion algorithms.      

基于CZT的多子带信号时差估计方法

针对稀疏多子带信号多子带综合时差估计难,高分辨时差估计计算量大的问题,提出了一种基于线性调频Z变换(CZT)的稀疏多子带信号融合的快速高分辨时差估计算法。该方法通过CZT对各子带信号的互谱进行高分辨的谱分析得到各子带信号的高分辨互相关函数,通过分析各子带互相关函数的相位关系实现各子带互相关函数的相参积累。相比传统广义互相关算法,该方法在实现多子带相参积累的同时,大大降低了计算量。仿真结果表明:提出的基于CZT的多子带融合快速时差估计方法能精确地估计时差,相比单子带信号的时差估计性能可以获得明显提升。     

Non-binary Sparse Measurement Matrices for Binary Signal Recovery

Binary sparse measurement matrices are widely used in compressed sensing (CS) due to their low computational complexity. However, binary sparse measurement matrices perform well in CS-based binary signal recovery only when the source signals are very sparse (e.g., k/n=0.1, where k is the sparsity of the source signal, n is the length of the source signal). In this paper, we propose to construct a non-binary sparse measurement matrix to recover binary source signals which are not so sparse (e.g., k/n=0.2) accurately with few measurements. The novel measurement matrix enables us to design a suboptimal and effective recovery algorithm by fully exploiting the structural features. Moreover, we analyze and estimate the un-recovery probability based on the tree structure to evaluate the recovery performance. The simulation results validate that non-binary sparse measurement matrices can be used to recover binary source signals which are not so sparse, the recovery performance of non-binary sparse measurement matrices is better than that of binary sparse measurement matrices in terms of the un-recovery probability.