Abstract: Since the traditional wavelet threshold functions have some drawbacks such as the non-continuity on the points of threshold, large deviation of estimated wavelet coefficients, Gibbs phenomenon and distortion are generated and Signal-to-Noise Ratio (SNR) can be hardly improved for the denoised signal. To overcome these drawbacks, an improved wavelet threshold function was proposed. Compared with the soft, hard, semi-soft threshold function and others, this function was not only continuous on the points of threshold and more convenient to be processed, but also was compatible with the performances of traditional functions and the practical flexibility was greatly improved via adjusting dual threshold parameters and dual variable factors. To verify this improved function, a series of simulation experiments were performed, the SNR and Root-Mean-Square Error (RMSE) values were compared between different denoising methods. The experimental results demonstrate that the smoothness and distortion are greatly enhanced. Compared with soft function, its SNR increases by 22.2% and its RMSE decreases by 42.6%.

Key words: wavelet transform, threshold function, Signal-To-Noise Ratio (SNR), Root-Mean-Square Error (RMSE), denoising

摘要： 针对传统的小波阈值函数在阈值处不连续、小波估计系数存在偏差等不足,导致去噪后的信号产生吉布斯振荡、失真和信噪比(SNR)无法提高等问题,提出了一种改进的小波阈值函数去噪方法。与传统的软、硬阈值和半软阈值等函数相比,该函数不仅在阈值处连续,便于运算处理,而且由于双阈值变量和双可变因子的引入,使得该函数既兼容了传统阈值函数的优点,还可以通过调节双阈值和双因子,来提高实际应用的灵活性。为了验证该阈值函数的优越性,通过仿真实验并对比几种小波去噪方法的信噪比和均方根误差,实验结果表明,经本阈值函数去噪后的信号在平滑度和失真度上有较大改善,相比软阈值函数,信噪比提高了22.2%,均方根误差减小了42.6%。

关键词: 小波变换, 阈值函数, 信噪比, 均方根误差, 去噪