离散混沌测量矩阵构造及其性能研究

若测量矩阵满足约束等距性(restricted isometric property, RIP),则样本能够完美恢复出原始信号。而对于给定矩阵很难验证其是否满足RIP需求,因此,本文采用李雅普诺夫指数作为一种针对离散混沌测量矩阵的验证指标。首先分析了RIP与李雅普诺夫指数之间的联系,然后给出了一种分段式混沌映射构造方法用以提高混沌性能,并从理论和仿真上证明了该方法的有效性。实验结果表明,这种方法不仅提高了混沌序列的随机性和自相关性,而且所生成的测量矩阵也具有更好的性能。因此,引进李雅普诺夫指数是一种有效的验证离散混沌测量矩阵性能的方法,提高李雅普诺夫指数能够提高混沌测量矩阵的性能。

Construction and performance research of discrete chaotic measurement matrix

If the sampling matrix has the restricted isometric property (RIP), the samples will contain enough information to recover the original signal extremely well. Actually, the RIP requirement is hard to verify for a given matrix. Therefore, the Lyapunov exponent as the metric is used to verify the performance of the discrete chaotic measurement matrix. Firstly, the relationship between the RIP and the Lyapunov exponent is analyzed, and a segmentation method is proposed for improving the performance of the chaotic map, then its validity is proved by theory and numerical results. The present results show that the method can both increase the Lyapunov exponent of chaotic map and improve the performance of the generated measurement matrix. Obviously, the Lyapunov exponent is a good metric to verify the performance of the discrete chaotic measurement matrix. By increasing the value of the Lyapunov exponent, the performance of the chaotic measurement matrix can be improved easily.