基于局部线性相关的信号去噪方法

针对基于整体线性逆问题的信号去噪方法会导致信号去噪不充分以及严重丢失细节的问题,提出一种建立在局部线性相关基础上的信号去噪方法。该方法以带噪声信号与原始信号局部存在线性相关性为基础,首先利用信号局部具有相同的尺度系数与偏移量,构造信号匹配模型；然后以原始信号的1-范数构造正则项；最后利用快速收缩算法求解去噪模型,使收敛速度达到二阶收敛。实验结果表明,本文方法稳定性强、鲁棒性好,在去噪的同时较好的恢复了信号的高频分量。

Signal denoising algorithm based on local linear correlation

The signal denoising algorithm based on linear inverse problem will lead to inadequate denoise and serious loss of details. In order to overcome this problem, the signal denoising algorithm based on local linear correlation was proposed. This method is based on the local linear correlation between the original signal and the noise signal. Firstly, the signal matching model is constructed by using the same scaling factor and offset in local area. Then, the regular term is constructed with the 1- norm of the original signal. Finally, a fast iterative shrinkage-thresholding algorithm is proposed to find the solution, with the convergence speed is quadratic convergence. The experimental results show that the method is robust and fast. Specifically, the proposed method is to eliminate the noise at the same time it is better to restore the high frequency component of the signal.