采样列化的切比雪夫混沌测量矩阵构造算法研究
发布时间：2018-07-13 15:29
【摘要】：压缩感知利用信号的稀疏性,无损地从低维测量信号中恢复高维度稀疏信号。然而,目前存在的测量矩阵中大多存在元素相关性高等问题,无法保证恢复效果的精确性,大大制约了它们的应用前景。针对此问题,通过引入切比雪夫混沌系统,提出一种基于采样列化的切比雪夫混沌感知测量矩阵(SC3M)。不同于经典的相对独立取值的构造方法,SC3M矩阵通过对切比雪夫混沌序列作采样列化及归一化处理等操作来确保矩阵的低列相关性,以优化重构效果;进一步,结合Johnson-Lindenstrauss引理严格证明了其满足约束等距特性(restricted isometric property,RIP),给提出的测量矩阵的应用提供了扎实的理论依据。实验仿真表明,提出的混沌测量矩阵能确保良好的信号和图像重构精度,明显优于纯随机矩阵、伯努利矩阵和高斯矩阵等其他经典测量矩阵。
[Abstract]:Compression perception utilizes the sparsity of the signal to recover the high dimensional sparse signal from the low dimensional measurement signal. However, there are many problems in the measurement matrix, such as high correlation of elements, which can not guarantee the accuracy of the recovery effect, which greatly restricts their application prospects. To solve this problem, a Chebyshev chaotic sensing measurement matrix (SC3M) based on sampling listing is proposed by introducing Chebyshev chaotic system. In order to optimize the reconstruction effect, the SC3M matrix, which is different from the classical construction method of relatively independent values, can ensure the low column correlation of the matrix by sampling and normalizing the Chebyshev chaotic sequence. In combination with Johnson-Lindenstrauss Lemma, it is strictly proved that it satisfies the constraint isometric characteristic (restricted isometric propertyn RIP), which provides a solid theoretical basis for the application of the proposed measurement matrix. Experimental results show that the proposed chaotic measurement matrix can ensure good signal and image reconstruction accuracy, and is superior to other classical measurement matrices such as pure random matrix, Bernoulli matrix and Gao Si matrix.
【作者单位】： 广州大学松田学院;广东农工商职业技术学院;中国移动通信集团广东有限公司;
【基金】：广东省省级课题资助项目(GDYJSKT16-08) 广东省高等职业教育教学改革立项课题(201401154)
【分类号】：TN911.7
本文编号：2119891
[Abstract]:Compression perception utilizes the sparsity of the signal to recover the high dimensional sparse signal from the low dimensional measurement signal. However, there are many problems in the measurement matrix, such as high correlation of elements, which can not guarantee the accuracy of the recovery effect, which greatly restricts their application prospects. To solve this problem, a Chebyshev chaotic sensing measurement matrix (SC3M) based on sampling listing is proposed by introducing Chebyshev chaotic system. In order to optimize the reconstruction effect, the SC3M matrix, which is different from the classical construction method of relatively independent values, can ensure the low column correlation of the matrix by sampling and normalizing the Chebyshev chaotic sequence. In combination with Johnson-Lindenstrauss Lemma, it is strictly proved that it satisfies the constraint isometric characteristic (restricted isometric propertyn RIP), which provides a solid theoretical basis for the application of the proposed measurement matrix. Experimental results show that the proposed chaotic measurement matrix can ensure good signal and image reconstruction accuracy, and is superior to other classical measurement matrices such as pure random matrix, Bernoulli matrix and Gao Si matrix.
【作者单位】： 广州大学松田学院;广东农工商职业技术学院;中国移动通信集团广东有限公司;
【基金】：广东省省级课题资助项目(GDYJSKT16-08) 广东省高等职业教育教学改革立项课题(201401154)
【分类号】：TN911.7
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