基于压缩感知的混沌系统重构的应用研究

发布时间：2018-04-05 05:11

本文选题：压缩感知　切入点：混沌系统　出处：《东北大学》2014年硕士论文

【摘要】：基于时间序列的混沌动态系统估计问题在非线性动力学上是一个十分突出的问题,传统的标准延迟坐标嵌入方法无法保证高的重构精度。而近年来十分引人注目的压缩感知理论提供了一个新颖的框架,其核心思想是由原始信号经线性投影得到的少量的观测值中重构稀疏的信号。它重构原始信号所需要的测量值远远少于传统的信号处理框架,尤其是在观测值不充足的情况下,更是成为了获得较高重构精确度的重要选择。在这样的背景下,将压缩感知与混沌系统重构相结合就显得尤为有意义。本文首先介绍了最近提出的一种具有广泛意义的方法,即仅有少量时间序列值可以获取的情况下,基于压缩感知的框架就可以重构混沌系统方程,包括其中重要参数的值。该方法在非线性系统预测上具有启发性的价值,它可以被应用到很多涉及到非线性结构的领域中。已经有科研人员将其应用在了预测灾难性的分岔行为,探测网络中的未知节点以及隔热时变系统的未来状态等。本文在这些基础上,创新性地将这一方法应用到了两种热点关注领域,即光学信息安全技术领域中的密码系统,以及杜芬系统的弱信号检测中。(1)在我们提出的密码系统中,两对由网络映射生成的相位-振幅掩膜被应用到4f双随机相位-幅值编码(DRPAE)系统中来进行图像加密。与以往的传送真正的密钥值以及大量的掩码不同的是,仅有非常少量的从掩膜中选取的不连续观测点被传送至解码端。我们恰当地修改了网络映射方程的序列展开项来更好地逼近混沌系统。那么基于压缩感知的框架,混沌方程也就可以重构出来,加密系统的密钥值就可以成功地估算出来,从而重新生成正确的解密掩膜。仿真实验表明该密码系统具有很大的优势,表现在占用很少量的密码传送空间及无需传送所有的密钥值从而提高了加密的安全性。(2)将混沌系统重构的问题拓展到了杜芬振子对弱正弦信号的频率进行检测上,由于传统的检测单正弦信号频率的方法需要较为严格的要求,存在内策动力的频率与待测微弱信号相对频差的绝对值要小于0.03rad/s以及对未知频率的微小信号检测效率较低的问题。而基于压缩感知的杜芬系统重构的方法可以较好地解决这些问题。
[Abstract]:The problem of chaotic dynamic system estimation based on time series is a very prominent problem in nonlinear dynamics. The traditional standard delayed coordinate embedding method can not guarantee high reconstruction accuracy.In recent years the theory of compression sensing provides a novel framework whose core idea is to reconstruct sparse signals from a small number of observations obtained by linear projection of the original signal.The measurement value needed to reconstruct the original signal is far less than that of the traditional signal processing framework, especially in the case of insufficient observations, which is an important choice to obtain higher reconstruction accuracy.In this context, it is particularly meaningful to combine compression perception with chaotic system reconstruction.In this paper, we first introduce a recently proposed method that can reconstruct chaotic system equations, including the values of important parameters, when only a small number of time series values can be obtained.This method is of enlightening value in nonlinear system prediction and can be applied to many fields involving nonlinear structures.Some researchers have applied it to predict catastrophic bifurcation behavior, detect unknown nodes in the network and the future state of heat-insulated time-varying systems.Based on these results, this paper creatively applies this method to two hot areas of concern, namely, cryptosystem in the field of optical information security and weak signal detection in Duffin system.Two pairs of phase-amplitude masks generated by network mapping are applied to 4f double random phase-amplitude coded DRPAE systems for image encryption.Different from the real key values and a large number of masks in the past, only a very small number of discontinuous observation points selected from the mask are transmitted to the decoding end.We modify the sequence expansion term of the network mapping equation to better approximate the chaotic system.Then the chaotic equation can be reconstructed based on the frame of compression perception and the key value of the encryption system can be estimated successfully so that the correct decryption mask can be generated again.The simulation results show that this cryptosystem has great advantages.The problem of chaotic system reconstruction is extended to detect the frequency of weak sinusoidal signal by Duffin oscillator.Because the traditional method of detecting the frequency of single sinusoidal signal requires strict requirements, the absolute value of the relative frequency difference between the internal driving force and the weak signal to be measured is smaller than that of 0.03rad/s, and the detection efficiency of the small signal with unknown frequency is low.The method of reconstructing Duffin system based on compressed perception can solve these problems well.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.4;O415.5

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