基于最优分解尺度的静态提升小波去噪方法

阈值函数选择和分解尺度确定是基于阈值的小波域非线性滤波的两个关键步骤。针对加性白噪声的情况,通过研究小波阈值去噪原理,得出了重构信号信噪比随分解尺度的单增变化规律,构造了用于指示最优分解尺度的目标函数;在分析白噪声小波系数高斯分布特性的基础上,提出了一种基于概率理论的阈值函数,通过极小化广义阈值估计偏差函数,得到了该阈值函数中参数的最优分布区间。仿真结果表明,构造的目标函数能够准确指示信号分解的最优尺度,广泛适用于硬阈值类函数;新阈值函数与另外两种改进型阈值函数相比,在信噪比意义下表现出一定的优越性。

Stationary Lifting Wavelet De-noising Method Based on Optimal Decomposition Level

The selection of threshold function and determination of decomposition level are two key steps in threshold-based nonlinear filtering by wavelet transform. In the presence of additive white noise, the variation rule of reconstructed signal SNR is concluded via research into the theory of wavelet threshold de-noising, and a target function is accordingly built to indicate the optimal decomposition level. Based on analysis of white noise wavelet coefficients distribution characteristic, a novel threshold func...