压缩传感理论、优化算法及其在系统状态重构中应用

发布时间：2018-01-15 04:30

本文关键词：压缩传感理论、优化算法及其在系统状态重构中应用　出处：《信息与控制》2017年03期 　论文类型：期刊论文

【摘要】：分别对压缩传感理论、优化算法及其在系统状态重构中的应用3个方面进行了研究.在压缩传感理论方面,包括对所压缩信号的稀疏或低秩要求、编码测量以及与优化算法之间的关系进行了较为深入的研究,重点分析了原始信号的稀疏与低秩之间的关系、测量矩阵与压缩矩阵之间的关系、满足限制等距特性(RIP)的测量矩阵,以及由压缩传感理论提供的最少测量次数.在压缩信号重构过程中所需要采用的优化算法,着重讨论了核函数的凸优化问题描述,分别对常用的优化算法,包括最小二乘(LS)法、最大熵法、极大似然法和贝叶斯方法的求解过程中所用到的性能指标、优化目标和求解条件等进行了归纳与特性分析.对量子态估计中的交替方向乘子法(ADMM)以及作者最新提出的迭代阈值收缩法(IST)进行了专门的性能对比,并通过量子位分别5、6和7情况下纯态估计的应用为例,对不同测量比率对参数估计性能的影响,以及算法在不同量子位数下性能的表现,进行了不同层次上的对比和分析,完整地阐述基于压缩传感理论与优化的系统参数估计的研究过程.
[Abstract]:Three aspects of compression sensing theory, optimization algorithm and its application in system state reconstruction are studied respectively. In compression sensing theory, the sparse or low rank requirements of compressed signals are included. The relationship between the coding measurement and the optimization algorithm is deeply studied, and the relationship between the sparse and low rank of the original signal and the relation between the measurement matrix and the compression matrix is analyzed. The minimum number of measurements provided by the compression sensing theory and the optimization algorithm needed in the process of compression signal reconstruction. The convex optimization problem description of kernel function is discussed in detail. The common optimization algorithms, including the least square LSmethod and the maximum entropy method, are discussed respectively. The performance indexes used in the solution of maximum likelihood method and Bayesian method. The optimization objectives and solving conditions are summarized and analyzed. The alternating direction multiplier method in quantum state estimation and the iterative threshold contraction method (IST) proposed by the authors are discussed. A special performance comparison is made. The effects of different measurement ratios on the performance of the parameter estimation and the performance of the algorithm under different quantum bits are given by the application of pure state estimation in the case of 5 qubits and 7 qubits respectively. The research process of system parameter estimation based on compression sensing theory and optimization is described by comparison and analysis at different levels.
【作者单位】：中国科学技术大学信息科学技术学院;
【基金】：国家自然科学基金资助项目(61573330)
【分类号】：TN911.7
【正文快照】： 1引言压缩传感(compressive sensing)理论是对稀疏信号数据同时进行采样、压缩和恢复的理论,该理论将嵌在高维空间中的输入信号,变换成维数较小空间中的信号,并在获取信号的同时对数据进行适当的压缩,然后再利用合适的重建算法,对压缩的数据进行信号恢复[1].2006年Can-des和Do

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