| Since2007, when the compressed sensing theory came out, the relative researches appeared one by one, the theory can be developed by the sparsity of signal, through random sampling to obtain a sample of holographic discrete signal in the far smaller than the Nyquist sampling rate requirement, then reconstructed signal perfectly use the nonlinear method. The theory has put forward has aroused widespread concern in the scientific community and industry, at the same time, it was applied to signal processing, medicine, astronomy, data mining and same other fields.This paper describes the compressed sensing based on the existing research in detail, combined with the characteristics of chaotic system, this paper put forward the idea of chaotic compressed sensing, established a set of evaluation system to realize the chaotic compressed sensing, then the chaotic compressed sensing theory was applied to the signal encryption and network topology identification.In the aspect of theoretical research, this paper takes the stochastic properties of chaotic sequence and the compressed sensing measurement matrix as a similar point, and built the model of chaotic compressed sensing, and compared the effect with the traditional compressed sensing. Because of the realization of the effect of model is mainly determined by the sampling method of chaotic sequence, this paper have discussed the different influence of sampling situation (chaotic system, chaotic state, the sampling interval, initial value etc.), to the reconstruction result of compressed sensing (feasibility, effect, accuracy) in detail, and realized the quantitative assessment of the result of compressed sensing from many aspects.On the application aspect, this paper realizes the application of chaos of compressed sensing in information security and network topology identification.Combined with the characteristics of chaotic system (pseudo randomness, boundedness and initial value sensitivity) and related properties of compressed sensing measurement matrix (random, boundedness), this paper applied the chaotic compressed sensing to the signal security encryption. The existing measurement matrix is mainly composed of a random function (Gauss function, Bernoulli function and so on) generated values constitute, but due to the above similar characteristics, this paper use the chaotic system to construct the corresponding sampling sequence measurement matrix for signal encryption, the initial value of chaotic system is the decryption key. Compared with the traditional compressed sensing method for signal encryption, the key produced by this method is very small, and very sensitive, it greatly improves the efficiency of transmission, storage and encryption. In this paper, we establish an application framework of chaotic compressed sensing in the field of information security, and deeply discussed the feasibility, safety and scenarios.Because there are many complex networks with chaotic characteristics, in the network topology identification application, this paper sampled the values of the output of each node in the network, to estimate the unknown part of the network edge basing on these data. For some connections of the complex network weights are unknown, the network topology identification process can be transformed into a sparse vector solving problems of equation through mathematical derivation. Therefore, this paper proposes for identification applying compressed sensing theory on complex networks for the first time, and achieved good results in the identification accuracy and efficiency. At the same time, this paper introduces information entropy, which is used to measure the state of the network, and it provides a way to estimate the feasibility and accuracy of identification.The application of the above two aspects are an independent application framework, this paper describe elements of process of scheme and Simulation of the effect of assessment scheme, this scheme can be independently applied to a variety of real scene. For information security, chaotic compressed sensing can be applied to real-time monitoring of video encryption transmission, it applies to the extreme conditions such as the deep space and deep sea. In the field of network identification, the method can be used for identification of complex network structure, which presents a variety of chaotic characteristics. |
