经验模态分解构造观测矩阵的方法

doi:10.3969/j.issn.1001-2400.2018.01.007

摘要/Abstract

摘要：

为了大概率地保持信号信息的完整性，观测矩阵被设计得倾向于随机矩阵．但这种随机性也导致有用的信息和无用的信息被接近等概率地测量，降低了感知效率．为了提高观测效率，提出了利用参考信号进行经验模态分解构造观测矩阵的方法——本征模函数循环矩阵．基于Gersgorin圆盘定理证明了该矩阵满足约束等距性条件．以信号降噪效果为衡量标准，仿真了该矩阵的信号降噪过程，结果表明，为参考信号添加一定程度的噪声后形成的观测矩阵，对降噪有更佳的效果; 对于含噪信号与参考信号在时域有错位的情况，虽然在时域上的降噪效果与理想情况有明显的降低，但仍能够更好地凸显信号的频域特征，具有实用价值．

关键词: 观测矩阵, 压缩感知, 信号降噪, 稀疏重构, 循环矩阵

Abstract:

In order to maintain the integrity information on the signal in high probability, the measuremental matrix is designed to be a random one. But this randomness results in the fact that both useful information and useless information are near the equiprobably measured, which leads to a low sensing efficiency. To improve the sensing efficiency, this paper proposes a new method of measurement matrix construction based on Empirical Mode Decomposition of the reference signal. It uses the Intrinsic Mode Function to construct a cyclic matrix, which is proved to satisfy the restricted isometry property condition by the Gersgorin disc theorem. It simulates the signal denoising process and uses signal noise reduction as the measure. Simulation results show: (1)it has a better effect on reducing noise by adding noise to the reference signal; (2)when the noisy signal and the reference signal are dislocated in the time domain, the effect of noise reduction is significantly decreased compared with the ideal condition. However, the reconstructed signal maintains its frequency information well, which is helpful in practical applications.

Key words: measurement matrix, compressive sensing, signal denosing, sparse reconstruction, circulant matrix

刘学文;肖嵩;薛晓. 经验模态分解构造观测矩阵的方法[J]. 西安电子科技大学学报, 2018, 45(1): 35-41.

LIU Xuewen;XIAO Song;XUE Xiao. Measurement matrix construction based on empirical mode decomposition[J]. Journal of Xidian University, 2018, 45(1): 35-41.

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