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1、中南民族大学 硕士学位论文 压缩感知在无线传感器网络中的应用研究 姓名：瞿毅 申请学位级别：硕士 专业：通信与信息系统 指导教师：朱翠涛 2011-05-16 中南民族大学硕士学位论文 I 摘 要 摘 要 随着无线传感器网络规模扩大，能量消耗、数据流量增大等问题越显突出。 压缩采样技术的出现为解决这些问题提供了一种有效途径，因此，成为目前研究 的一个热点。本文将压缩感知技术应用于无线传感器网络中，作了如下几个方面 的研究工作。 针对无线传感器网络中信号的恢复精度问题，本文在正交匹配追踪算法、正 则化匹配追踪算法以及稀疏度自适应匹配追踪算法基础上综合得到一种改进的稀 疏度自适应匹配追踪恢复算法。
2、该算法的主要思想是：在整个迭代过程中，首先， 求解当前阶段中数量固定的最大相关系数所对应原子索引来构建候选集，再在其 基础上选出满足正则化要求的原子索引集，然后根据已选的索引集，采用相同的 方法得到数量固定的最大相关系数索引值来构建支撑集，将支撑集对应的原子集 进行正交化处理，并根据新支撑集恢复稀疏信号，求解残余值，最后比较前后两 次的残余值二范数，对应的更新迭代段索引、选择最大相关系数的数量、残余值， 一直到满足停止条件为止。通过软件实验的仿真，将改进算法与稀疏自适应匹配 追踪恢复算法相比较，在一定的噪声干扰下，改进算法能够精确恢复原始信号， 其成功恢复概率提高了10%左右，且具有良好的抗噪
3、特性。 在无线传感器网络中信号恢复基础上，为了研究如何提高网络中检测处于工 作状态稀疏节点的概率，本文分析压缩感知基本原理和L1范数最小化问题，得到 一种改进的下降迭代检测算法。该算法的主要思想是：设置一个最大的迭代次数， 每一次进入迭代之前，将本次迭代的次数与最大值比较。如果大于最大值，就停 止迭代；否则，继续迭代。每次迭代得到的解都会加入一个具有调节作用的因子， 然后将其倒数作为下一次迭代的权值。在整个迭代过程中，若迭代次数未达到最 大值，但满足阈值条件，就停止迭代；若迭代次数达到最大值，但不满足阈值条 件，就强制停止。软件仿真结果表明，与贝叶斯检测算法相比较，在相同观测点 数情况下，改进
4、的权值迭代算法能够以较大概率检测0-1二元制稀疏信号，其成功 检测概率提高了约13%；在稀疏度相同的情况下，改进算法的检测概率提高了20% 左右。 关键词：无线传感器网络；压缩感知；信号的重构；稀疏事件检测；关键词：无线传感器网络；压缩感知；信号的重构；稀疏事件检测； 压缩感知在无线传感器网络中的应用研究 II ABSTRACT With the expansion of the scale of wireless sensor networks, the problem about energy consumption accelerating and data traffic increa
5、sing will become more prominent. Compressed sampling technology provides an effective method to resolve these issues, which is a research hotspot, now. Compressed sensing technology is used in wireless sensor networks in the paper, and the following aspects are researched. For the problem of the pre
6、cision recovery of the signal in wireless sensor networks, the paper proposes an advanced sparsity adaptive matching pursuit recovery algorithm based on orthogonal matching pursuit algorithm, regularized orthogonal matching pursuit algorithm, sparsity adaptive matching pursuit algorithm. The main id
7、ea of the improved algorithm is as follows: In the whole iterative process, first of all, the index of atoms will be solved corresponding to a fixed number of the maximum correlation coefficient, then built the candidate set in this stage. Based on the selected candidate index, some set will be prod
8、uced via regularization condition. According to the selected index set, the same method is used to get the support index set from a fixed number of the maximum values of the correlation coefficient. Corresponding to the support set, the atoms will be orthogonalized, from which the sparse signal is r
9、ecoveried, then the residual value is calculated. At last, the values of residual about the former and the latter are compared. Then the iteration stage index, the size of select the largest correlation coefficient, the residual value, are updated. The algorithm will continue iterating until the con
10、diton is met. Software simulation experiments show that, compared improved algorithm with sparity adaptive matching pursuit algorithm, Under a certain noise, the improved algorithm can accurately recovery the original signal, the probability of its success can reach about 10%, and has a good anti-no
11、ise characteristic. Based on signal recovery in wireless sensor networks, in order to study how to improve the probablity of the detection of working states sparse nodes, the paper adopt the compressed sensing technology and analyzes the minimum L1 norm, then proposes a kind of advanced decline iter
12、ative detection algorithm. The algorithm of the specific implementation is as follows: A maximum number of iterations is set, before entering some iteration, the advanced algorithm compares the number of this iteration with the maximum value. If the number of this iteration is greater than the maxim
13、um value, the iteration will be suspended; Otherwise, continue iterating. At each iteration, the factor would be added to the solution to regulate the weight, then the reciprocal of the sum of the solution and the factor will be given to next weight value. In the whole processing, 中南民族大学硕士学位论文 III i
14、f the number of iteration doesnt reach to the set maximum value, the threshold conditions is met, it will stop the iterative; if the number of iteration exceeds the set maximum value, the threshold conditions isnt met, it will stop the iterative at soon. The software simulation results show that, co
15、mpared with bayesian algorithm, under the same number of observation points, the improved iterative algorithm can detect the 0-1 binary sparse signal by high probability, and the probability of successful detection is improved by 13%; Under the same sparsity, the detection probability of the propose
16、d algorithm is improved about 20%. Keywords: wireless sensor networks; compressed sensing; signal reconstruction; the detection of sparse event 中南民族大学中南民族大学 学位论文原创性声明学位论文原创性声明 本人郑重声明：所呈交的论文是本人在导师的指导下独立进行研究所取 得的研究成果。除了文中特别加以标注引用的内容外，本论文不包含任何其 他个人或集体已经发表或撰写的成果作品。 对本文的研究做出重要贡献的个 人和集体，均已在文中以明确方式标明。本人完全意识到本声明的法律后果 由本人承担。 作者签名： 日期： 年 月 日 学位论文版权使用授权书学位论文版权使用授权书 本学位论文作者完全了解学校有关保留、使用学位论文的规定，同意学 校保留并向国家有关部门或机构送交论文的复印件和电子版， 允许论文被查 阅和借阅。 本人授权中南民族大学可以将本学位论文的全部或部分内容编入 有关数据库进行检索，可以采用影印、缩印或扫描等复制手段保存和
