基于類-LDPC測(cè)量的信號(hào)重構(gòu)算法及其應(yīng)用研究
發(fā)布時(shí)間：2018-08-01 10:38
【摘要】：壓縮感知(Compressive Sensing,CS)是近年來興起的一項(xiàng)新型的信號(hào)獲取技術(shù)。其突破之處在于利用信號(hào)的稀疏性,通過測(cè)量矩陣投影降低原始信號(hào)的維數(shù),獲得低維的測(cè)量值,再設(shè)計(jì)合適的重構(gòu)算法,從低維的測(cè)量值中恢復(fù)出原始信號(hào)。壓縮感知理論及相關(guān)技術(shù)要在實(shí)際應(yīng)用場(chǎng)景中獲得成功使用,需要解決的兩個(gè)關(guān)鍵問題就是降低壓縮感知系統(tǒng)的復(fù)雜度以及克服噪聲影響獲得信號(hào)的準(zhǔn)確重構(gòu)。低密度奇偶校驗(yàn)碼(Low-density parity check,LDPC)的校驗(yàn)矩陣本身具有稀疏性且矩陣元素僅有0和1兩種取值,作為壓縮感知的測(cè)量矩陣可以降低系統(tǒng)復(fù)雜度。壓縮感知技術(shù)由于其突破奈奎斯特采樣定理的限制極大地壓縮數(shù)據(jù),在醫(yī)學(xué)圖像成像、遙感、通信信道估計(jì)、頻譜檢測(cè)、無線傳感器網(wǎng)絡(luò)等多個(gè)領(lǐng)域的應(yīng)用也極具前景。因此,本文從提高壓縮感知技術(shù)的實(shí)用性出發(fā),對(duì)采用類-LDPC校驗(yàn)矩陣作為稀疏測(cè)量矩陣的壓縮感知系統(tǒng)進(jìn)行研究,重點(diǎn)圍繞其在噪聲環(huán)境下的信號(hào)重構(gòu)算法設(shè)計(jì)展開研究。同時(shí),作為壓縮感知技術(shù)在應(yīng)用領(lǐng)域的一種嘗試,本文對(duì)無線傳感器網(wǎng)絡(luò)中基于壓縮感知的數(shù)據(jù)收集方法進(jìn)行了探索,從降低系統(tǒng)的復(fù)雜度、延長(zhǎng)網(wǎng)絡(luò)生存時(shí)間出發(fā),基于所研究的低復(fù)雜度的類-LDPC稀疏測(cè)量壓縮感知模型,設(shè)計(jì)了一種應(yīng)用于無線傳感器網(wǎng)絡(luò)的壓縮數(shù)據(jù)收集方案。論文首先針對(duì)D.Baron的置信傳播重構(gòu)算法(Compressive Sensing Belief Propagation,CSBP)進(jìn)行研究,并針對(duì)其重構(gòu)精度受限問題進(jìn)行了改進(jìn)。CSBP算法將壓縮測(cè)量過程等效為一個(gè)類-LDPC碼的編碼過程,基于二分圖進(jìn)行置信傳播(Belief Propagation,BP)計(jì)算得到條件邊緣概率和信號(hào)值的最小均方誤差(Minimum Mean Square Error,MMSE)近似估計(jì)。本文在研究中發(fā)現(xiàn)由于類-ⅠLDPC編碼并不嚴(yán)格滿足LDPC校驗(yàn)矩陣的條件,造成算法在進(jìn)行BP解碼時(shí)具有一定的發(fā)散概率,解出的邊緣概率并未收斂到最優(yōu)值；另外CSBP算法利用BP解碼的結(jié)果直接進(jìn)行信號(hào)值的近似MMSE估計(jì),以上兩個(gè)因素導(dǎo)致了CSBP算法重構(gòu)精度受限。為了解決這一問題,本文對(duì)CSBP算法進(jìn)行了以下改進(jìn)：增加了支撐集檢測(cè)的步驟,以置信傳播計(jì)算出信號(hào)的MMSE近似估計(jì)值XMMSE(t)作為支撐集檢測(cè)的初值,建立動(dòng)態(tài)的判決門限選取機(jī)制,通過信號(hào)元素值與門限的比較檢測(cè)出信號(hào)的支撐集I(r)；再根據(jù)獲取的支撐集選擇合適的信號(hào)值估計(jì)方法重新對(duì)信號(hào)的非零元素取值進(jìn)行估計(jì)。針對(duì)二維圖像信號(hào)重建的實(shí)驗(yàn)結(jié)果表明,相比于CSBP算法,改進(jìn)的方法具有更高的重構(gòu)精度和更快的收斂速度。其次為了提高重建算法的適應(yīng)性,論文針對(duì)Jaewook K.等人的一種有噪環(huán)境下的貝葉斯支撐集檢測(cè)(Bayesian Support Detection,BSD)算法進(jìn)行了研究和改進(jìn)。BSD算法基于原始稀疏信號(hào)服從一維高斯分布的假設(shè),采用二元假設(shè)檢驗(yàn)概率模型判斷出信號(hào)的支撐集,因此其性能優(yōu)勢(shì)主要體現(xiàn)在對(duì)一維高斯分布信號(hào)的重建精度上。為了使重建能夠同時(shí)適應(yīng)高斯和非高斯分布的稀疏信號(hào),本文對(duì)BSD算法進(jìn)行了改進(jìn),提出了一種基于回溯和置信傳播的信號(hào)重構(gòu)算法：在支撐集檢測(cè)步驟,一方面利用BP迭代得到信號(hào)初值,通過非線性算子計(jì)算出初始的信號(hào)支撐；再引入類似子空間搜索的回溯思想,因?yàn)椴捎昧艘徊交厮莸倪^程,使得支撐集的檢測(cè)上更加優(yōu)化；并且對(duì)信號(hào)值的估計(jì)也采用了和BSD不同的方法。以上改進(jìn)使重構(gòu)過程中的支撐集檢測(cè)和非零元素估計(jì)都不需要限制稀疏信號(hào)的分布狀態(tài)為高斯分布,因而對(duì)非高斯分布的稀疏信號(hào)也能夠進(jìn)行高精度的重建。本文分別針對(duì)一維高斯和二維圖像信號(hào)進(jìn)行仿真實(shí)驗(yàn),結(jié)果表明相對(duì)于BSD方法,本文提出的采用了回溯和置信傳播的方法對(duì)于高斯和非高斯分布信號(hào)的重建都能夠獲得較高的重建精度和更快的收斂速度。以簡(jiǎn)化壓縮測(cè)量過程為目的,本文將卡爾曼濾波過程引入置信傳播的信號(hào)重構(gòu)算法中,利用卡爾曼濾波進(jìn)行信號(hào)值估計(jì)；為了降低濾波計(jì)算的復(fù)雜度,本文在卡爾曼濾波過程中采用動(dòng)態(tài)的測(cè)量矩陣,根據(jù)每次BP迭代獲得的支撐集檢測(cè)結(jié)果,動(dòng)態(tài)設(shè)定卡爾曼濾波方程組中的測(cè)量矩陣ΦT,以低維矩陣運(yùn)算代替原來的高維矩陣；并基于類-LDPC壓縮測(cè)量模型分析了算法的收斂性和誤差。實(shí)驗(yàn)結(jié)果表明,基于卡爾曼濾波的置信傳播重構(gòu)算法能夠在低測(cè)量矩陣稀疏率和較少的測(cè)量次數(shù)的情況下獲得較高的重構(gòu)精度。最后,論文將基于類-LDPC稀疏測(cè)量的壓縮感知模型應(yīng)用于無線傳感器網(wǎng)絡(luò)(Wireless Sensor Networks,WSNs),針對(duì)現(xiàn)有無線傳感器網(wǎng)絡(luò)數(shù)據(jù)收集多采用單天線的傳輸策略,造成傳輸?shù)哪芰看鷥r(jià)過大,傳輸丟包率高易出錯(cuò)的問題,設(shè)計(jì)了一種基于類-LDPC稀疏測(cè)量的WSNs虛擬MIMO (Multiple Input Multiple Output)壓縮數(shù)據(jù)收集方案,其特征在于結(jié)合了類.LDPC稀疏測(cè)量和MIMO傳輸技術(shù),首先建立數(shù)據(jù)收集的系統(tǒng)模型和能量消耗模型Etotal,其次依據(jù)能量最優(yōu)原則對(duì)網(wǎng)絡(luò)的分簇?cái)?shù)目nc、壓縮測(cè)量矩陣的稀疏率β和壓縮比ρ、參與協(xié)作傳輸?shù)墓?jié)點(diǎn)數(shù)目M以及遠(yuǎn)程傳輸時(shí)調(diào)制的星座圖大小b進(jìn)行聯(lián)合優(yōu)化,獲取各優(yōu)化參數(shù)值(β，ρ,nc,Mt,b),根據(jù)優(yōu)化參數(shù)配置測(cè)量矩陣Φ,設(shè)計(jì)虛擬MIMO傳輸方案。相比于單天線的多路由傳輸策略,本文的方法能夠根據(jù)網(wǎng)絡(luò)的節(jié)點(diǎn)數(shù)目和覆蓋區(qū)域,降低數(shù)據(jù)收集過程中的傳輸能耗和丟包率,從而能提高無線傳感網(wǎng)的數(shù)據(jù)收集效率,延長(zhǎng)網(wǎng)絡(luò)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.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TN911.7
[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.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TN911.7
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