基于稀疏表示的TQWT在低频振荡信号去噪中应用

为了改善低频振荡信号的去噪效果，为低频振荡信号的检测与分析提供准确可靠的数据，在分析可调Q小波变换和稀疏表示原理的基础上，给出了一种基于稀疏表示的可调Q小波变换去噪方法。该方法先利用可调Q小波变换对含噪的低频振荡信号进行稀疏分解，得到初始的小波系数。再利用基追踪去噪算法对得到的小波系数进行优化处理。最后对优化的小波系数进行重构，获取干净无噪的低频振荡信号。通过仿真分析验证了该方法的去噪效果和可靠性优于目前广泛使用的小波软、硬阈值去噪法。

Low frequency oscillating signals denoising based on TQWT via sparse representation

In order to improve the denoising effect of low frequency oscillation signals and provide the accurate and reliable data for detection and analysis of low frequency oscillation signals, the denoising method based on tunable Q-factor wavelet transform via sparse representation is given on the analysis of tunable Q-factor wavelet transform and sparse representation theories. Firstly, the tunable Q-factor wavelet transform is adopted to perform the signal sparse decomposition for the noisy low frequency oscillation signals, and the initial wavelet coefficients are obtained; secondly, the BP denoising algorithm is used to optimize the obtained wavelet coefficients; lastly, the optimized wavelet coefficients are reconstructed, then the low frequency oscillation signal without noisy is obtained. After the computer simulation, the result demonstrates that this method is superior to the current widely used wavelet soft-threshold and hard-threshold in denoising effect and reliability.