基于类-LDPC测量的信号重构算法及其应用研究

发布时间：2018-08-01 10:38

【摘要】：压缩感知(Compressive Sensing,CS)是近年来兴起的一项新型的信号获取技术。其突破之处在于利用信号的稀疏性,通过测量矩阵投影降低原始信号的维数,获得低维的测量值,再设计合适的重构算法,从低维的测量值中恢复出原始信号。压缩感知理论及相关技术要在实际应用场景中获得成功使用,需要解决的两个关键问题就是降低压缩感知系统的复杂度以及克服噪声影响获得信号的准确重构。低密度奇偶校验码(Low-density parity check,LDPC)的校验矩阵本身具有稀疏性且矩阵元素仅有0和1两种取值,作为压缩感知的测量矩阵可以降低系统复杂度。压缩感知技术由于其突破奈奎斯特采样定理的限制极大地压缩数据,在医学图像成像、遥感、通信信道估计、频谱检测、无线传感器网络等多个领域的应用也极具前景。因此,本文从提高压缩感知技术的实用性出发,对采用类-LDPC校验矩阵作为稀疏测量矩阵的压缩感知系统进行研究,重点围绕其在噪声环境下的信号重构算法设计展开研究。同时,作为压缩感知技术在应用领域的一种尝试,本文对无线传感器网络中基于压缩感知的数据收集方法进行了探索,从降低系统的复杂度、延长网络生存时间出发,基于所研究的低复杂度的类-LDPC稀疏测量压缩感知模型,设计了一种应用于无线传感器网络的压缩数据收集方案。论文首先针对D.Baron的置信传播重构算法(Compressive Sensing Belief Propagation,CSBP)进行研究,并针对其重构精度受限问题进行了改进。CSBP算法将压缩测量过程等效为一个类-LDPC码的编码过程,基于二分图进行置信传播(Belief Propagation,BP)计算得到条件边缘概率和信号值的最小均方误差(Minimum Mean Square Error,MMSE)近似估计。本文在研究中发现由于类-ⅠLDPC编码并不严格满足LDPC校验矩阵的条件,造成算法在进行BP解码时具有一定的发散概率,解出的边缘概率并未收敛到最优值；另外CSBP算法利用BP解码的结果直接进行信号值的近似MMSE估计,以上两个因素导致了CSBP算法重构精度受限。为了解决这一问题,本文对CSBP算法进行了以下改进：增加了支撑集检测的步骤,以置信传播计算出信号的MMSE近似估计值XMMSE(t)作为支撑集检测的初值,建立动态的判决门限选取机制,通过信号元素值与门限的比较检测出信号的支撑集I(r)；再根据获取的支撑集选择合适的信号值估计方法重新对信号的非零元素取值进行估计。针对二维图像信号重建的实验结果表明,相比于CSBP算法,改进的方法具有更高的重构精度和更快的收敛速度。其次为了提高重建算法的适应性,论文针对Jaewook K.等人的一种有噪环境下的贝叶斯支撑集检测(Bayesian Support Detection,BSD)算法进行了研究和改进。BSD算法基于原始稀疏信号服从一维高斯分布的假设,采用二元假设检验概率模型判断出信号的支撑集,因此其性能优势主要体现在对一维高斯分布信号的重建精度上。为了使重建能够同时适应高斯和非高斯分布的稀疏信号,本文对BSD算法进行了改进,提出了一种基于回溯和置信传播的信号重构算法：在支撑集检测步骤,一方面利用BP迭代得到信号初值,通过非线性算子计算出初始的信号支撑；再引入类似子空间搜索的回溯思想,因为采用了一步回溯的过程,使得支撑集的检测上更加优化；并且对信号值的估计也采用了和BSD不同的方法。以上改进使重构过程中的支撑集检测和非零元素估计都不需要限制稀疏信号的分布状态为高斯分布,因而对非高斯分布的稀疏信号也能够进行高精度的重建。本文分别针对一维高斯和二维图像信号进行仿真实验,结果表明相对于BSD方法,本文提出的采用了回溯和置信传播的方法对于高斯和非高斯分布信号的重建都能够获得较高的重建精度和更快的收敛速度。以简化压缩测量过程为目的,本文将卡尔曼滤波过程引入置信传播的信号重构算法中,利用卡尔曼滤波进行信号值估计；为了降低滤波计算的复杂度,本文在卡尔曼滤波过程中采用动态的测量矩阵,根据每次BP迭代获得的支撑集检测结果,动态设定卡尔曼滤波方程组中的测量矩阵ΦT,以低维矩阵运算代替原来的高维矩阵；并基于类-LDPC压缩测量模型分析了算法的收敛性和误差。实验结果表明,基于卡尔曼滤波的置信传播重构算法能够在低测量矩阵稀疏率和较少的测量次数的情况下获得较高的重构精度。最后,论文将基于类-LDPC稀疏测量的压缩感知模型应用于无线传感器网络(Wireless Sensor Networks,WSNs),针对现有无线传感器网络数据收集多采用单天线的传输策略,造成传输的能量代价过大,传输丢包率高易出错的问题,设计了一种基于类-LDPC稀疏测量的WSNs虚拟MIMO (Multiple Input Multiple Output)压缩数据收集方案,其特征在于结合了类.LDPC稀疏测量和MIMO传输技术,首先建立数据收集的系统模型和能量消耗模型Etotal,其次依据能量最优原则对网络的分簇数目nc、压缩测量矩阵的稀疏率β和压缩比ρ、参与协作传输的节点数目M以及远程传输时调制的星座图大小b进行联合优化,获取各优化参数值(β，ρ,nc,Mt,b),根据优化参数配置测量矩阵Φ,设计虚拟MIMO传输方案。相比于单天线的多路由传输策略,本文的方法能够根据网络的节点数目和覆盖区域,降低数据收集过程中的传输能耗和丢包率,从而能提高无线传感网的数据收集效率,延长网络的生存周期。
[Abstract]:Compressive Sensing (CS) is a new signal acquisition technology in recent years. Its breakthrough is to use the sparsity of the signal to reduce the dimension of the original signal through the measurement of the matrix projection, obtain the low dimensional measurement value, and then design a suitable reconstruction algorithm to recover the original signal from the low dimensional measurement value. The two key problems to be solved are to reduce the complexity of the compressed sensing system and to reconstruct the signal from the noise influence. The parity check matrix of the Low-density parity check (LDPC) is of sparsity and moments. The array element has only 0 and 1 values. As a measurement matrix of compressed sensing, the complexity of the system can be reduced. Compressed sensing technology has greatly compressed data because of its breakthrough Nyquist sampling theorem. It has also been applied in many fields, such as medical image imaging, remote sensing, communication channel estimation, spectrum detection, wireless sensor network and so on. Therefore, this paper, starting from the practicability of improving the compression sensing technology, studies the compressed sensing system using the -LDPC check matrix as a sparse measurement matrix, focusing on the design of the signal reconstruction algorithm in the noise environment. At the same time, as an attempt of the compressed sensing technology in the field of application, this paper is on the basis of this paper. The method of data collection based on compressed sensing is explored in wireless sensor networks. From reducing the complexity of the system and prolonging the lifetime of the network, a compressed data collection scheme applied to wireless sensor network is designed based on the low complexity -LDPC sparse measurement compression perception model of low complexity. The Compressive Sensing Belief Propagation (CSBP) algorithm for D.Baron is studied, and the coding process of the compressed measurement process is equivalent to a class -LDPC code based on the improved.CSBP algorithm, which is based on the two partite graph to obtain the conditional edges of the packet propagation (Belief Propagation, BP). The approximate estimation of the minimum mean square error (Minimum Mean Square Error, MMSE) of the marginal probability and the signal value. In this paper, we find that because the class I LDPC code does not strictly satisfy the condition of the LDPC check matrix, the algorithm has a certain divergence probability during BP decoding, and the edge probability of the solution does not converge to the optimal value; moreover, the CSBP calculation is also calculated. The method uses the result of BP decoding to direct the approximate MMSE estimation of the signal value. The above two factors lead to the limitation of the reconstruction precision of the CSBP algorithm. In order to solve this problem, the following improvements are made to the CSBP algorithm: the step of the support set detection is added, and the MMSE approximate estimation value XMMSE (T) is supported by confidence propagation as the support. The dynamic decision threshold selection mechanism is set up, and the support set I (R) of the signal is detected by the comparison of the signal element value and the threshold, and then the non zero element value of the signal is estimated again by the selection of the appropriate signal value estimation method of the acquired support set. The experimental results of the two-dimensional image signal reconstruction show that the phase signal is reconstructed. Compared with the CSBP algorithm, the improved method has higher reconstruction precision and faster convergence speed. Secondly, in order to improve the adaptability of the reconstruction algorithm, the paper studies and improves the Bayesian Support Detection (BSD) algorithm in a noisy environment of Jaewook K. et al. And improves the.BSD algorithm based on the original sparse letter. According to the assumption of one dimension Gauss distribution, the two element hypothesis test probability model is used to determine the support set of the signal, so its performance advantage is mainly reflected in the reconstruction precision of one dimension Gauss distribution signal. In order to make the reconstruction adapt to the sparse signal of Gauss and non Gauss distribution, this paper improves the BSD algorithm. A signal reconstruction algorithm based on backtracking and confidence propagation: in the support set detection step, on the one hand, the initial signal value is obtained by BP iteration, the initial signal support is calculated by the nonlinear operator, and the backtracking thought similar to the subspace search is introduced, because the process of one step backtracking makes the detection of the support set better. And the estimation of the value of the signal is also different from the BSD. The above improvement makes the support set detection and non zero element estimation in the reconfiguration process do not need to restrict the distribution of the sparse signal to Gauss distribution, so the sparse signal of the non Gauss distribution can also be reconstructed with high precision. The simulation experiments of the two dimensional image signal show that the method proposed in this paper can obtain high reconstruction precision and faster convergence speed for the reconstruction of Gauss and non Gauss distributed signals relative to the BSD method. In order to simplify the compression measurement process, the Calman filter is used in this paper. In the signal reconstruction algorithm of confidence propagation, Calman filter is used to estimate the signal value. In order to reduce the complexity of the filter calculation, this paper uses a dynamic measurement matrix in the Calman filtering process, and dynamically sets the measurement matrix of the Calman filter equation group (T), according to the result of the support set obtained from each BP iteration. The low dimensional matrix operation is used to replace the original high dimensional matrix, and the convergence and error of the algorithm are analyzed based on the class -LDPC compression measurement model. The experimental results show that the reconstruction algorithm of confidence propagation based on Calman filter can obtain higher reconstruction precision in the condition of low measurement matrix sparsity and less measurement times. Finally, the theory of reconstruction of confidence propagation can be obtained. In this paper, the compressed sensing model based on -LDPC like sparse measurement is applied to wireless sensor network (Wireless Sensor Networks, WSNs). For the data collection of existing wireless sensor networks, the transmission strategy of single antenna is adopted, the energy cost of transmission is too large and the transmission loss rate is high and error prone. A kind of -LDPC thinning based on class -LDPC is designed. The sparse measurement WSNs virtual MIMO (Multiple Input Multiple Output) compression data collection scheme is characterized by combining the.LDPC sparse measurement and MIMO transmission technology of the class.LDPC. First, the system model of data collection and the energy consumption model Etotal are established. Secondly, the clustering number of the network is followed by the number of NC with the energy optimal principle, and the sparse measurement matrix is sparse. The rate beta and compression ratio rho, the number of nodes involved in the cooperative transmission M and the constellation size B of the remote transmission are optimized jointly to obtain the optimal parameter values (beta, rho, NC, Mt, b). A virtual MIMO transmission scheme is designed based on the optimized parameter configuration measurement matrix. Compared with the single antenna multi route transmission strategy, the method of this paper can base on the method. The number of nodes and coverage area of the network reduces the transmission energy consumption and packet loss rate in the process of data collection, thus improving the data collection efficiency of the wireless sensor network and prolonging the lifetime of the network.
【学位授予单位】：安徽大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN911.7

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