基于Lipschitz指数的小波阈值去噪方法

Wavelet Threshold De-noising Method Based on Lipschitz Exponent

对于非平稳信号,小波多尺度分解是一种有效的信号去噪工具。在D.L.Donoho的多分辨率小波阈值去噪方法的基础上,提出了基于Lipschitz指数的小波阈值去噪方法。仿真结果表明,采用基于Lipschitz指数的小波阈值去噪方法不仅有效抑制了由于硬阈值函数的不连续性而在信号奇异点附近产生的Pseudo-Gibbs现象,而且在更加彻底去噪的前提下很好地保留了信号的边缘信息。无论是在视觉效果上,还是在信噪比增益和最小均方误差意义上均优于传统的软硬阈值方法。

Wavelet multi-scale decomposition is an effective method to eliminate the noises for unstable signals. In virtue of the multi-resolution wavelet threshold de-noising method presented by D. L. Donoho, the wavelet threshold de-nosing method with the use of Lipschitz exponent was proposed. Simulation results indicate that this method can effectively suppress the Pseudo-Gibbs phenomena in the vicini- ties of the singular points of the signal due to the discontinuity of the hard threshold function. It also reserves the edge information of the signals under the condition of thorough elimination of noises. Numerical results also show that this method gives better MSE performance and SNR gains than both the traditional hard threshold and soft threshold methods.