受污染混沌信号的协同滤波降噪

根据混沌吸引子的自相似分形特性,提出了一种利用协同滤波重构受污染混沌信号的降噪算法.所设计的降噪算法通过对相似片段的分组将一维混沌信号的降噪转化为一个二维联合滤波问题;然后,在二维变换域用阈值法衰减噪声;最后,通过反变换获得原始信号的估计.由于分组中的相似片段具有良好的相关性,与直接在一维变换域做阈值降噪相比,分组的二维变换能获得原信号更稀疏的表示,更好地抑制噪声.仿真结果表明,该算法对原始混沌信号的重构精度和信噪比的提升都优于小波阈值、局部曲线拟合等现有的混沌信号降噪方法,对相图的还原质量也更好.

Denoising of contaminated chaotic signals based on collaborative filtering

Reconstructing chaotic signals from noised data plays a critical role in many areas of science and engineering. However, the inherent features, such as aperiodic property, wide band spectrum, and extreme sensitivity to initial values, present a big challenge of reducing the noises in the contaminated chaotic signals. To address the above issues, a novel noise reduction algorithm based on the collaborative filtering is investigated in this paper. By exploiting the fractal self-similarity nature of chaotic attractors, the contaminated chaotic signals are reconstructed subsequently in three steps, i.e., grouping, collaborative filtering, and signal reconstruction. Firstly, the fragments of the noised signal are collected and sorted into different groups by mutual similarity. Secondly, each group is tackled with a hard threshold in the two-dimensional (2D) transforming domain to attenuate the noise. Lastly, an inverse transformation is adopted to estimate the noise-free fragments. As the fragments within a group are closely correlated due to their mutual similarity, the 2D transform of the group should be sparser than the one-dimensional transform of the original signal in the first step, leading to much more effective noise attenuation. The fragments collected in the grouping step may overlap each other, meaning that a signal point could be included in more than one fragment and have different collaborative filtering results. Therefore, the noise-free signal is reconstructed by averaging these collaborative filtering results point by point. The parameters of the proposed algorithm are discussed and a set of recommended parameters is given. In the simulation, the chaotic signal is generated by the Lorenz system and contaminated by addictive white Gaussian noise. The signal-to-noise ratio and the root mean square error are introduced to measure the noise reduction performance. As shown in the simulation results, the proposed algorithm has advantages over the existing chaotic signal denoising methods, such as local curve fitting, wavelet thresholding, and empirical mode decomposition iterative interval thresholding methods, in the reconstruction accuracy, improvement of the signal-to-noise ratio, and recovering quality of the phase portraits.