基于切比雪夫扩频序列的循环测量矩阵构造算法(研究生论坛)

在分布式多节点应用场景中, 针对需要产生大量混沌序列来构造测量矩阵造成资源和通信带宽浪费的缺点，提出了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。利用符号函数把由切比雪夫混沌函数产生的序列进行二值化得到扩频序列，选择一定长度的序列作为一行循环生成测量矩阵，并证明了由循环生成的序列满足贝努利分布。选取一维信号和二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，在相同的压缩比下，新矩阵在一维信号上的恢复效果与其他矩阵相同，在二维红外图像和自然图像中，相比于其他矩阵具有更好的恢复效果。

Circulating measurement matrix construction algorithm based on Chebyshev spreading sequence

In the distributed application scenario, as the shortcoming of resources and communication bandwidth wasting caused by a large number of chaotic sequences, which constructed the measurement matrix, a algorithm of structuring circulating measurement matrix was put forward based on Chebyshev spread spectrum sequence, in which Chebyshev chaotic function was used to generate the sequence and the spread spectrum sequence got by the symbol function, generated the measurement matrix by circulating the spread spectrum sequence. At last, the sequence by circulating was proved obeying the Bernoulli distribution. Simulation results show that Compared with Chebyshev Bernoulli matrix, Bernoulli matrix , Gaussian matrix and Logistics chaotic matrix, under the same compression ratio, a new matrix on one-dimensional signal had the same recovery effect as other matrix, but had the better recovery effect on the 2d infrared image and nature image.