非高斯噪声背景下小波阈值算法分析

摘要

A new threshold function under non-Gaussian noise background was presented to overcome the limitations of wavelet threshold algorithm under the Gaussian noise background. The shortcomings of conventional function, such as discontinuity of hard threshold function and the invariable dispersion of soft threshold function, can be solved. The new function which employed high order power function was put forward based on Garrote threshold. First, the signal with a class of non-Gaussian noise was decomposed by wavelet. Secondly, each high frequency wavelet coefficient was quantified based on new threshold function. Thirdly, signal was reconstructed by the low frequency coefficients of wavelet decomposition and quantified high frequency coefficients. The simulation results under non-Gaussian noise background indicate that the new threshold function gets higher Signal-to-Noise Ratio (SNR) gains and lower minimum Mean Square Error (MSE) compared to the soft and hard threshold,two types of improved threshold and Garrote threshold.%针对小波阈值算法以高斯噪声为研究背景的局限性,为解决硬阈值函数不连续和软阈值函数估计小波系数和分解小波系数存在恒定偏差的问题,在非高斯噪声背景下提出一种新的小波阈值算法.新阈值函数从Garrote阈值改进而来,引入了高阶幂函数.该算法首先对加入一类非高斯噪声的信号进行小波分解,然后根据新的阈值函数对每层高频小波系数进行量化,最后用小波分解的低频系数和处理过的高频系数重构信号.在非高斯噪声背景下进行的仿真结果表明,新阈值函数去噪相对于软阈值、硬阈值、两类改进阈值以及Garrote阈值在信噪比和最小均方误差上都得到了改善.