基于小波模极大值移位相关的光谱去噪方法

A Denoising Algorithm for Absorption Spectra by Wavelet Transform Modulus Maxima Shift-Related Filter

提出一种小波模极大值移位相关滤波算法,用来对吸收光谱进行去噪处理。首先,依据小波变换模极大值理论,识别吸收光谱的二进小波系数中的噪声成分和有用信号成分;然后将其中相邻尺度的有用成分在波数轴上移位对齐,修正模极大值在尺度间的"漂移"现象,并对其中噪声成分进行平滑;最后将预处理后的相邻尺度的小波子带相乘,根据得到的小波系数尺度间的相关度,进一步强化信号的重要特征,同时衰减噪声。相比SSNF及MPTH等去噪方法,新的算法不需要估计噪声强度,可避免引入误差和复杂计算;也不需要进行迭代计算,可消除算法收敛缓慢甚至不收敛的危险;同时,该算法修正了光谱谱峰在不同尺度的模极大值位置的"漂移",可弥补这一现象造成的谱信息的损失。实验结果证明,提出的滤波算法在保留SF6气体红外吸收光谱的有用成分的前提下,有效的滤除了噪声。

In the present paper, a wavelet modulus maximum shift--related filter algorithm is proposed for denoising the absorption spectra. Firstly, using the wavelet transform modulus maxima theory, useful signal components and noise components of the binary wavelet coefficients of absorption spectra are identified. Then, the useful signal components are aligned in the wave number domain to correct the ＂drifting＂ of modulus maximum across the scales, and the noise components are smoothed. Finally, according to the wavelet interscale dependencies obtained by multiplying the adjacent wavelet subbands preprocessed by the above procedure, important features of signal are enhanced while noises are attenuated further. Compared with the traditional spatially selective noise filtration technique proposed by Xu et al and adaptive multiscale products thresholding technique proposed by Paul Bao et al, the proposed wavelet modulus maximum shift--related filter algorithm has several advantages. First, it does not need estimate of the noise intensity, which could avoid the error introducing and the complex calculation. Meanwhile, there is not iterative calculation in the proposed algorithm, which could eliminate the risk of slow convergence or no convergence of the algorithm. Furthermore, the ＂drifting＂ of modulus maximum across the scales could be corrected in the proposed algorithm, which could make up for the loss of the spectrum information caused by the ＂drifting＂ phenomenon. Experiments show that the proposed scheme can effectively suppress noise and preserve the useful components in the infrared absorption spectra of SF6 gas.