基于新阈值函数的二进小波变换信号去噪研究

由于二进小波变换的小波基函数存在着一定的冗余,基于二进小波变换的去噪效果要好于离散小波变换的信号去噪·噪声阈值的准确估计和阈值函数的选择对去噪精度有着显著的影响·在分析高斯噪声的二进小波变换特性基础上,提出了一种改进的二进小波变换去噪方法·采用一种新的阈值函数,克服了Donoho软阈值方法中估计小波系数与分解小波系数存在恒定偏差的缺陷·仿真结果表明,改进的二进小波去噪方法不仅可以有效地抑制信号奇异点处的pseudo-Gibbs现象,而且消噪精度高于传统的软硬阈值方法·

Signal De-noising Research Based on New Threshold Function via Dyadic Wavelet Transform

There is a certain redundancy in the primary function of wavelet for dyadic wavelet transform. So, the de-noising result by dyadic wavelet transform is better than that by discrete wavelet transform. How to estimate the noise threshold and select the threshold function exactly will affect obviously the de-nosing accuracy. Analyzing the characteristics of the dyadic wavelet transform of Gaussian noise, a new approach to signal de-noising is proposed to improve the dyadic wavelet transform by introducing a new threshold to get rid of the constant error when using Donoho's soft threshold to estimated and decompose the wavelet coefficients. Simulation results indicate that the new approach will not only suppress effectively the pseudo-Gibbs phenomena at the singular point of signal waveform, but provide a higher de-noising accuracy than Donoho' s hard and soft-threshold methods.