基于切比雪夫扩频序列的循环测量矩阵构造算法

发布时间：2018-08-16 13:49

【摘要】：在分布式多节点应用场景中,针对需要产生大量混沌序列构造测量矩阵造成资源和通信带宽浪费的缺点,提出一种基于切比雪夫扩频序列的分布式循环测量矩阵构造算法。首先,根据分布式网络中节点的个数,在接收端利用切比雪夫函数产生相应长度的混沌序列,通过广播的方式广播给网络中的各个节点,节点利用改进的乘同余法选择相应的序列段作为该节点的混沌序列;然后,各个节点利用符号函数把混沌序列进行二值化得到扩频序列,选择一定长度的扩频序列作为一行循环生成测量矩阵;最后,证明了由循环生成的序列满足贝努利分布。选取1维信号和2维图像进行仿真实验。结果表明:相比于切比雪夫贝努利矩阵、贝努利矩阵、高斯矩阵和罗切斯特混沌矩阵,在相同的测量值下,新方法构造的矩阵在1维信号上的恢复效果与其他矩阵相同;在2维红外图像和自然图像中,新方法构造的矩阵相比于其他矩阵具有更好的恢复效果。
[Abstract]:In the distributed multi-node application scenario, a distributed cyclic measurement matrix construction algorithm based on Chebyshev spread spectrum sequence is proposed to solve the problem that a large number of chaotic sequences are needed to construct measurement matrix, which results in waste of resources and communication bandwidth. Firstly, according to the number of nodes in the distributed network, the Chebyshev function is used to generate chaotic sequences of corresponding length at the receiving end, which is broadcast to each node in the network. The node selects the corresponding sequence segment as the chaotic sequence of the node by using the improved multiplicative congruence method, and then, each node uses the symbol function to binary the chaotic sequence to obtain the spread spectrum sequence. The spread spectrum sequence of a certain length is chosen as the measurement matrix of a row of cyclic generation. Finally, it is proved that the sequence generated by the cycle satisfies the Bernoulli distribution. 1 D signal and 2 D image are selected for simulation experiment. The results show that compared with Chebyshev Bernoulli matrix, Gao Si matrix and Rochester chaotic matrix, under the same measurement value, the recovery effect of the matrix constructed by the new method on 1-D signal is the same as that of other matrices. In 2D infrared images and natural images, the matrix constructed by the new method is more effective than other matrices.
【作者单位】：四川大学电子信息学院;
【基金】：四川省科技支撑计划项目资助(2016GZ0091)
【分类号】：TN911.7

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