用信道编码构造压缩感知测量矩阵

压缩感知是近年来,针对稀疏信号和可压缩信号的处理而出现的一种信号处理理论。测量矩阵是压缩感知理论中的一个至关重要的环节,它对信号采样和重构算法有着重要的影响。虽然一般传统的随机测量矩阵重建信号效果比较好,但有硬件实现比较困难的问题,并需要大量的存储空间和其他缺陷。确定性测量矩阵的出现,正好弥补了这些缺点。在本文中,基于信道编码中校验矩阵特性的优势,获得了满足有限紧致特性要求的确定性测量矩阵构造方法。把校验矩阵的列向量标准化、线性组合扩展到方阵、置换列向量后构成的矩阵作为确定性测量矩阵。这种方法可以在构造完成一个信道编码校验矩阵后,很容易构造对应的测量矩阵。数值结果表明,在相同重建算法和压缩比下,这种方法的性能和随机测量矩阵大致相若,甚至有所改善。同时,本文提出方法的构造时间较少,重建时只需要运行一次,可以满足实时性需求。为压缩感知算法的实际应用提供了一种有效的测量矩阵构造方法。      

改进的压缩感知测量矩阵优化方法

压缩感知理论中,测量矩阵优化是一类通过减小测量矩阵与稀疏字典的互相关性来改善测量矩阵性能的方法。本文提出一种能够同时降低整体相关系数和最大值相关系数的测量矩阵优化算法,该算法分为两步:一是通过平均化Gram矩阵特征值来降低测量矩阵的整体相关系数;二是利用阈值函数收缩Gram矩阵非对角线上较大值。两个步骤交替执行,直到解出符合优化要求的测量矩阵。该算法在保证整体相关系数降到最低的同时,又使最大值相关系数显著降低。实验结果表明,与现有算法进行对比,本文方法在降低相关系数和重构成功率上都有一定优势。      

基于二进制序列族的压缩感知测量矩阵构造

构造确定性测量矩阵对压缩感知理论的推广与应用具有重要的意义。该文源于代数编码理论,提出一种基于二进制序列族的确定性测量矩阵构造算法。相关性是描述矩阵性质的重要准则,减小相关性可使重建性能提高。该文推导出所构造测量矩阵的相关性小于同条件下的高斯随机矩阵和伯努利随机矩阵。理论分析和仿真实验表明,该方式构造的测量矩阵的重建性能优于同条件下的高斯随机矩阵和伯努利随机矩阵;所构造矩阵可由线性反馈移位寄存器结构实现,易于硬件实现,有利于压缩感知理论的实用化。     

用于压缩感知的二值化测量矩阵

压缩感知是近年新兴的一种信号处理理论,在一定条件满足的情况下,压缩感知方法可通过远低于 Nyquist 频率的降采样数据以高概率近乎完美地重建原始信号。测量矩阵在压缩感知的整个处理过程中起着非常重 要的作用。本文从恢复算法入手提出二值化测量矩阵,并通过仿真对其性能加以验证。二值化后测量矩阵不仅在 性能上有一定提升,更重要的是可大大降低测量矩阵所需的存储空间以及压缩感知采样、恢复过程的运算量。     

压缩感知伪随机动态功率信号的电能测量方法

针对压缩感知检测方法不能准确测量伪随机动态测试信号电能量值的问题,该文首先分析了动态测试信号的频域稀疏性,证明动态测试信号满足压缩感知检测的条件;然后采用系统稳态优化的方法,构造了一种确定型压缩感知测量矩阵,证明其符合限制等距特性(RIP)条件,最后提出了一种新型压缩感知动态测试信号电能量的测量方法。实验结果表明：该文压缩感知测量方法的理论相对误差优于传统的采样功率电能测量方法,能够实现m序列动态测试信号的电能量值准确测量。     

基于随机矩阵理论的非重构宽带压缩频谱感知方法

该文采用随机矩阵理论(RMT)直接对压缩采样得到的观测数据进行分析,设计出了一种基于广义似然比检验(GLRT)的非重构宽带压缩频谱感知新算法。该算法无需任何先验知识就能对宽带频谱中的每个子带进行盲检测。此外,为了减轻次用户(SU)在数据获取和频谱感知过程中的通信开销,该文提出一种基于传感器节点(SN)辅助感知的合作频谱感知架构。理论分析和仿真结果均表明,与传统基于信号重构的GLRT感知算法以及Roy最大根检测(RLRT)算法相比,该算法不仅具有计算复杂度低、开销小、感知性能稳定等诸多优点;而且只需较少的SN就能获得较好的检测性能。     

压缩感知中测量矩阵与重建算法的协同构造

本文提出基于感知字典的迭代硬阈值(SDIHT)算法,以此协同构造压缩感知中测量矩阵与重建算法.将成对测量矩阵与感知字典分别用于压缩投影和构造重建算法,重建迭代至残差为零,从而精确恢复原始稀疏信号.本文证明了SDIHT算法精确恢复原始稀疏信号的充分条件.SDIHT算法的优点是重建精度高和计算复杂度低.仿真实验表明,当信号稀疏度或测量次数相同时,相比IHT、OMP和BIHT算法,SDIHT算法重建0-1稀疏信号和二维图像效果更好、算法效率更高.     

分块的有序范德蒙矩阵作为压缩感知测量矩阵的研究

测量矩阵是压缩感知(Compressed Sensing, CS)的重要组成部分,确定性的测量矩阵易于硬件实现,但是重构信号的精度一般不如随机矩阵。针对这一缺点,该文提出并构造了一种新的确定性测量矩阵,称作分块的有序范德蒙矩阵。范德蒙矩阵具有线性不相关的性质,在此基础上加上分块操作和对元素进行有序排列得到的分块的有序范德蒙矩阵,实现了时域中的非均匀采样,特别适合于维数较大的自然图像信号。仿真实验表明,对于图像信号该矩阵具有远高于高斯矩阵的重构精度,可以作为实际中的测量矩阵使用。     

一种基于复合混沌映射的压缩感知测量矩阵构造方法研究

针对常用随机测量矩阵存在硬件实现困难的不足,提出一种基于复合混沌映射的压缩感知确定性测量矩阵构造方法.首先基于Logistic映射和Tent映射构造随机性和初值敏感性更强的复合混沌映射,然后将复合混沌迭代序列经大间隔采样后进行线性变换得到的结果作为拟构造测量矩阵中的元素,并从理论上证明了该矩阵元素具有非常低的相关性.同时理论证明了所构造复合混沌测量矩阵能以高概率满足压缩感知约束等距性.实验结果表明,所构造复合混沌测量矩阵的性能优于Toeplitz测量矩阵及Logistic映射测量矩阵,与高斯随机测量矩阵的性能相仿.     

基于压缩感知的神经电信号测量方法设计

介绍了一种基于压缩感知的神经电信号采集方法,用于解决传统无线神经电信号采集系统面临的数据量及系统功耗的限制问题.鉴于压缩感知处理信号的稀疏性要求,该方法还可应用于其他生物电信号的采集、压缩,仿真验证压缩比可达10x,重建信号的信息损失较小.另外,由于以往神经电信号采集系统只截取动作电位中的一部分电位信息,因而存在信息损失现象;而本文方法可实现信号的连续采集.     

The high resolution MIMO radar system based on minimizing the statistical coherence of compressed sensing matrix

Compressed Sensing (CS) theory is a great breakthrough of the traditional Nyquist sampling theory. It can accomplish compressive sampling and signal recovery based on the sparsity of interested signal, the randomness of measurement matrix and nonlinear optimization method of signal recovery. Firstly, the CS principle is reviewed. Then the ambiguity function of Multiple-Input Multiple- Output (MIMO) radar is deduced. After that, combined with CS theory, the ambiguity function of MIMO radar is analyzed and simulated in detail. At last, the resolutions of coherent and non-coherent MIMO radars on the CS theory are discussed. Simulation results show that the coherent MIMO radar has better resolution performance than the non-coherent. But the coherent ambiguity function has higher side lobes, which caused a deterioration in radar target detection performances. The stochastic embattling method of sparse array based on minimizing the statistical coherence of sensing matrix is proposed. And simulation results show that it could effectively suppress side lobes of the ambiguity function and improve the capability of weak target detection.     

An adaptive measurement scheme based on compressed sensing for wideband spectrum detection in cognitive WSN

An Adaptive Measurement Scheme (AMS) is investigated with Compressed Sensing (CS) theory in Cognitive Wireless Sensor Network (C-WSN). Local sensing information is collected via energy detection with Analog-to-Information Converter (AIC) at massive cognitive sensors, and sparse representation is considered with the exploration of spatial temporal correlation structure of detected signals. Adaptive measurement matrix is designed in AMS, which is based on maximum energy subset selection. Energy subset is calculated with sparse transformation of sensing information, and maximum energy subset is selected as the row vector of adaptive measurement matrix. In addition, the measurement matrix is constructed by orthogonalization of those selected row vectors, which also satisfies the Restricted Isometry Property (RIP) in CS theory. Orthogonal Matching Pursuit (OMP) reconstruction algorithm is implemented at sink node to recover original information. Simulation results are performed with the comparison of Random Measurement Scheme (RMS). It is revealed that, signal reconstruction effect based on AMS is superior to conventional RMS Gaussian measurement. Moreover, AMS has better detection performance than RMS at lower compression rate region, and it is suitable for large-scale C-WSN wideband spectrum sensing.     

Cooperative MIMO spectrum sensing based on random matrix theory

Random Matrix Theory (RMT) is a valuable tool for describing the asymptotic behavior of multiple systems, especially for large matrices. In this paper, using asymptotic random matrix theory, a new cooperative Multiple-Input Multiple-Output (MIMO) scheme for spectrum sensing is proposed, which shows how asymptotic free property of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for Cognitive Radios (CRs). Simulations over Rayleigh fading and AWGN channels demonstrate the proposed scheme has better detection performance compared with the energy detection techniques even in the case of a small sample of observations.     

压缩感知在多源图像融合中的应用

针对全采样传统图像融合方法中计算量大、时间复杂度高的问题,提出了一种基于压缩感知(CS)理论的多源图像融合模型。为满足一定的稀疏性,将源图像在过完备二维离散余弦变换(DCT)字典上进行稀疏表示,并通过随机观测得到待融合的观测值;在每一图像块上采用基于标准差的方法自适应地计算融合权值,加权合成融合后的观测值,然后利用改进步长的梯度追踪算法求解稀疏系数,得到最终融合图像。实验结果表明：与传统方法相比,提出的融合模型在减少计算量和存储容量的同时,能更好地从源图像中提取信息,获得效果较好的融合图像。     

基于观测矩阵优化的自适应压缩频谱感知

推导了自适应压缩感知中的重构估算误差,研究了如何降低观测矩阵列向量之间的自相关性,分析了观测矩阵优化对压缩感知重构算法的影响。将观测矩阵优化与压缩感知自适应过程相结合,提出了基于观测矩阵优化的自适应压缩频谱感知算法。仿真结果证实,所提算法比传统算法重构时产生的均方误差(MSE)更低,在同一观测次数下检测概率更高,在达到同等接收操作性能(ROC)时所需观测次数更少。     

Novel method of moving target detection for dual-channel was radar based on compressed sensing

We propose a ground moving target detection method for dual-channel Wide Area Sur- veillance （WAS） radar based on Compressed Sensing （CS）. Firstly, the method of moving target detection of the WAS radar is studied. In order to reduce the sample data quantity of the radar, the echo data is randomly sampled in the azimuth direction, then, the matched filter is used to perform the range direction focus. We can use the compressive sensing theory to recover the signal in the Doppler domain. At last, the phase difference between the two channels is compensated to suppress the clutter. The result of the simulated data verifies the effectiveness of the proposed method.     

Adaptive sampling for compressed sensing based image compression

The compressed sensing (CS) theory has been successfully applied to image compression in the past few years as most image signals are sparse in a certain domain. In this paper, we focus on how to improve the sampling efficiency for CS-based image compression by using our proposed adaptive sampling mechanism on the block-based CS (BCS), especially the reweighted one. To achieve this goal, two solutions are developed at the sampling side and reconstruction side, respectively. The proposed sampling mechanism allocates the CS-measurements to image blocks according to the statistical information of each block so as to sample the image more efficiently. A generic allocation algorithm is developed to help assign CS-measurements and several allocation factors derived in the transform domain are used to control the overall allocation in both solutions. Experimental results demonstrate that our adaptive sampling scheme offers a very significant quality improvement as compared with traditional non-adaptive ones.     

A class of deterministic construction of binary compressed sensing matrices

Compressed Sensing (CS) is an emerging technology in the field of signal processing, which can recover a sparse signal by taking very few samples and solving a linear programming problem. In this paper, we study the application of Low-Density Parity-Check (LDPC) Codes in CS. Firstly, we find a sufficient condition for a binary matrix to satisfy the Restricted Isometric Property (RIP). Then, by employing the LDPC codes based on Berlekamp-Justesen (B-J) codes, we construct two classes of binary structured matrices and show that these matrices satisfy RIP. Thus, the proposed matrices could be used as sensing matrices for CS. Finally, simulation results show that the performance of the proposed matrices can be comparable with the widely used random sensing matrices.     

基于压缩感知信号重构的wifi室内定位算法研究

针对位置指纹定位算法在训练阶段信号数据采集量大和定位精度不高的问题,提出一种压缩感知(CS,Compressed Sensing)与K均值改进支持向量机(SVM,Support Vector Machine)相结合的定位算法模型(CS-KSVM)。CS算法在训练阶段利用已采集到的部分参考点wifi信号强度数据对整个指纹信号库进行重构以降低信号采集工作量,再用K均值改进SVM算法来实现测试点的准确分类。实验仿真结果表明,CS-KSVM算法在相同采样点条件下的定位精度明显要高于传统定位算法,同时在相同定位精度条件下大大减少了定位需要的采样点数。CS-KSVM算法在3米之内的定位准确度可以达到93.2%。