压缩采样信号检测及多任务重构算法研究

发布时间：2018-06-11 12:44

  本文选题：多任务 + 压缩感知　； 参考：《国防科学技术大学》2014年博士论文

【摘要】：卫星等信号侦收平台在数据存储、传输和处理资源上比较有限,研究如何解决这些问题有一定的意义,而压缩感知技术可以针对一般侦收信号的稀疏性特点进行有效的数据压缩和重构,对解决这一问题很有帮助,因此深入研究高效的稀疏信号重构算法具有一定的理论和现实意义。本文分别对压缩信号检测技术、多任务重构技术、多任务分类重构技术和合成多任务重构技术这四方面进行研究。论文的主要工作和创新点归纳如下:第二章基于NP准则对随机信号的压缩检测问题做了研究,给出了检测概率、虚警概率和检测门限三者的关系。分别研究了协方差为对角矩阵的高斯随机信号压缩检测问题,具有任意协协方差的高斯随机信号压缩检测问题和非高斯分布的随机信号检测问题。当观测样点数太少时,就不能正确的重构信号,但是对于压缩检测问题,较少的观测样点数就可以达到理想的检测概率。第三章针对多个压缩观测任务的原始信号属于同一类的情况,在贝叶斯框架下,提出了基于Laplace先验的多任务压缩感知算法(Laplace priors based Multitask Compressive Sensing,LMCS),是对单任务Laplace先验压缩感知算法的发展。分析了同MCS(Multitask Compressive Sensing,MCS)先验信息共享模型的不同,LMCS的贝叶斯框架比MCS的框架多了一层超先验信息,使得估计共享参数具有较大的灵活性,分析表明MCS是LMCS的特例。提出了基于Laplace先验多任务压缩感知的快速算法,把多余的噪声参数积分去掉,增强了算法的稳定性。证实了在针对一般性稀疏信号的贝叶斯重构算法中LMCS算法具有一定的优越性。然后针对模块化稀疏信号提出了一种联合重构算法,即EMBSBL(Extended Multitask Block Sparse Bayesian Learning,EMBSBL)算法。EMBSBL算法不仅利用信号间的统计相关性和信号内的模块化信息,而且重构时不需要模块稀疏信号的先验信息。第四章针对多个压缩观测任务的原始信号属于不同类的情况,提出了基于MDL(Minmum Description Length,MDL)准则的多任务分类重构算法。针对这种情况,如果不进行分类直接用LMCS或者MCS算法进行重构,导致重构性能很差。针对一般性稀疏信号进行分类重构,提出了基于MDL准则的MDL-LMCS和MDL-MCS算法,实验证实了该算法具有优越的分类和重构性能。然后针对于结构化稀疏信号,提出了新的分类重构算法,即GCEM-Turbo-GAMP-MMV算法,该算法利用状态演化特性来确定分类结果,然后对每类任务进行联合重构,在分类重构结构化稀疏信号方面优于MDL-LMCS和MDL-MCS算法。第五章针对模块化稀疏信号提出了一种合成多任务的压缩感知算法框架。多任务合成方法利用了模块化稀疏信号的特殊结构,通过对原始信号中元素和观测矩阵列的平移,合成多个新的任务,利用最小描述长度准则确定最佳的合成任务数,再采用多任务压缩感知算法重构原始信号,可以得到较好的重构性能。在多任务合成框架下,基于MCS算法和EMBSBL算法发展了新的合成多任务重构算法,分别简称为SMCS(Synthetic MCS,SMCS)算法和SEMBSBL(Synthetic EMBSBL,SEMBSBL)算法。这两种算法进行对比各有优缺点,SMCS算法运算时间少,但比后者重构精度差;SEMBSBL算法重构精度好,但运算量很大,这在处理大数据信号时尤为突出。两种合成多任务重构算法和其它单次重构算法对比的优点是不需要事先知道模块化稀疏信号的任何模块划分信息,并可以有效提高单次重构任务时的重构精度。
[Abstract]:The satellite signal detection platform is limited in data storage, transmission and processing resources. It is of certain significance to study how to solve these problems. And compressed sensing technology can effectively compress and reconstruct the sparse characteristics of the general detection signal. It is very helpful to solve this problem. The sparse signal reconstruction algorithm has some theoretical and practical significance. This paper studies the four aspects of compressed signal detection technology, multi task reconfiguration technology, multi task classification reconstruction technology and synthetic multi task reconstruction technology. The main work and innovation point of this paper are summarized as follows: the second chapter is based on the NP criterion for the compression of random signals. The relationship between detection probability, false alarm probability and detection threshold three is given. The problem of Gauss random signal compression detection with covariance matrix is studied. The problem of Gauss random signal compression detection with arbitrary covariance and random signal detection problem of non Gauss distribution, when the number of observation samples is too few The signal can not be reconstructed correctly, but for the problem of compression detection, fewer observation points can reach the ideal detection probability. In the third chapter, the original signal for multiple compression observation tasks belongs to the same class. In the Bias framework, a multi task compression sensing algorithm based on Laplace prior (Laplace prio) is proposed. RS based Multitask Compressive Sensing, LMCS) is the development of single task Laplace prior compression perception algorithm. The difference of sharing model with MCS (Multitask Compressive Sensing, MCS) prior information is analyzed. The analysis shows that MCS is a special case of LMCS. A fast algorithm based on Laplace prior multitask compression is proposed. The integral of the redundant noise parameters is removed and the stability of the algorithm is enhanced. It is proved that the LMCS algorithm is superior to the Bias reconstruction algorithm for general sparse signal. Then, the modular sparse signal is proposed. A joint reconstruction algorithm, namely, the EMBSBL (Extended Multitask Block Sparse Bayesian Learning, EMBSBL) algorithm.EMBSBL algorithm not only uses the statistical correlation between signals and modularized information within the signal, but also does not need the prior information of the sparse signal of the module. The fourth chapter is aimed at the original signal of multiple compression observation tasks. In the case of different classes, a multi task classification reconstruction algorithm based on the MDL (Minmum Description Length, MDL) criterion is proposed. In this case, the reconstruction performance is poor if the LMCS or MCS algorithm is rebuilt without classification. The classification and reconstruction of the general sparse letter numbers are classified and the MDL-LMCS based on MDL criterion is proposed. And MDL-MCS algorithm, the experiment proves that the algorithm has superior classification and reconfiguration performance. Then, a new classification reconstruction algorithm, called GCEM-Turbo-GAMP-MMV algorithm, is proposed for structured sparse signal. The algorithm uses the state evolution characteristics to determine the classification results, and then reconstructs each class of tasks jointly and structured in the classification reconstruction. The sparse signal is superior to the MDL-LMCS and MDL-MCS algorithms. In the fifth chapter, a multi task compression perceptual algorithm framework is proposed for modularized sparse signal. The multi task synthesis method utilizes the special structure of modularized sparse signal and synthesizes a number of new tasks by translation of elements and observation moments array in the original signal. The minimum description length criterion determines the optimal number of synthetic tasks, and then uses the multi task compression sensing algorithm to reconstruct the original signal, which can get better reconstruction performance. Under the framework of multi task synthesis, a new synthetic multitask reconstruction algorithm is developed based on MCS and EMBSBL algorithms, called SMCS (Synthetic MCS, SMCS) and SEMBSB, respectively. L (Synthetic EMBSBL, SEMBSBL) algorithm. The two algorithms have the advantages and disadvantages of each comparison. The SMCS algorithm has less operation time, but less precision than the latter. The SEMBSBL algorithm has a good reconstruction precision, but the computation is very large. It is particularly prominent in the processing of large data signals. The advantages of the two synthetic multitask reconfiguration algorithms and other single reconfiguration algorithms are compared. It is not necessary to know the modularity information of modular sparse signal beforehand, and it can effectively improve the reconfiguration accuracy of single reconfiguration task.
【学位授予单位】：国防科学技术大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN911.7

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