一种基于复合混沌映射的压缩感知测量矩阵构造方法研究
发布时间：2018-09-17 12:53
【摘要】：针对常用随机测量矩阵存在硬件实现困难的不足,提出一种基于复合混沌映射的压缩感知确定性测量矩阵构造方法.首先基于Logistic映射和Tent映射构造随机性和初值敏感性更强的复合混沌映射,然后将复合混沌迭代序列经大间隔采样后进行线性变换得到的结果作为拟构造测量矩阵中的元素,并从理论上证明了该矩阵元素具有非常低的相关性.同时理论证明了所构造复合混沌测量矩阵能以高概率满足压缩感知约束等距性.实验结果表明,所构造复合混沌测量矩阵的性能优于Toeplitz测量矩阵及Logistic映射测量矩阵,与高斯随机测量矩阵的性能相仿.
[Abstract]:In order to overcome the difficulties in hardware implementation of random measurement matrices, a method of constructing a compressed perceptual deterministic measurement matrix based on complex chaotic mapping is proposed. Based on Logistic map and Tent map, a complex chaotic map with more randomness and sensitivity to initial value is constructed, and then the result obtained by linear transformation of the iterative sequence of composite chaos after sampling at large intervals is regarded as the element in the quasi-constructed measurement matrix. It is proved theoretically that the matrix element has very low correlation. At the same time, it is proved theoretically that the constructed composite chaotic measurement matrix can satisfy the isometry of compressed perceptual constraints with high probability. The experimental results show that the performance of the constructed composite chaotic measurement matrix is superior to that of the Toeplitz measurement matrix and the Logistic mapping measurement matrix, which is similar to that of Gao Si random measurement matrix.
【作者单位】： 空军工程大学航空航天工程学院;北京机电工程研究所;
【分类号】：O151.21
本文编号：2245983
[Abstract]:In order to overcome the difficulties in hardware implementation of random measurement matrices, a method of constructing a compressed perceptual deterministic measurement matrix based on complex chaotic mapping is proposed. Based on Logistic map and Tent map, a complex chaotic map with more randomness and sensitivity to initial value is constructed, and then the result obtained by linear transformation of the iterative sequence of composite chaos after sampling at large intervals is regarded as the element in the quasi-constructed measurement matrix. It is proved theoretically that the matrix element has very low correlation. At the same time, it is proved theoretically that the constructed composite chaotic measurement matrix can satisfy the isometry of compressed perceptual constraints with high probability. The experimental results show that the performance of the constructed composite chaotic measurement matrix is superior to that of the Toeplitz measurement matrix and the Logistic mapping measurement matrix, which is similar to that of Gao Si random measurement matrix.
【作者单位】： 空军工程大学航空航天工程学院;北京机电工程研究所;
【分类号】：O151.21
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