基于多尺度Wiener滤波器的分形噪声滤波

针对淹没在1/f噪声中的有用信号恢复问题,本文提出了一套基于双正交小波变换与Wiener滤波的多尺度滤波算法,并设计出多尺度Wiener滤波器.首先,利用双正交小波变换将带有1/f噪声的信号分解成多尺度的子带信号,通过小波变换对1/f噪声的白化作用,消除了1/f噪声的非平稳性、自相似性和长程相关性.其次,在小波域内,利用Wiener滤波,实现了噪声和有用信号的分离,估计出了各子带中的有用信号.最后,利用双正交小波的精确重构性,较好地恢复出淹没在1/f噪声中的有用信号.仿真实验表明,该滤波器能有效的抑制分形噪声,显著地提高信噪比.

Multiscale Wiener Filter for the Estimation of Signal Embedded in 1/f Noise

f-Type noise,specially modeled by fractional Brownian motion (fBm) has attracted much attention in many fields.A multiscale Wiener filter based on biorthonormal wavelets and equipped with Wiener filter is proposed in this paper for signal restoration embedded in 1/f family of fractal signals.First,the signal with 1/f noise is transformed via the analysis filter bank into multiscale subsystems in time-scale domain based on biorthonormal wavelets.Some nostationary properties,e.g.self-similarity,long-term dependencies of fractal signals are attenuated in each subband by wavelet multiresolution decomposition so that the Wiener filter bank can be applied to estimate the multiscale input signals.Then the estimated multiscale input signals are synthesized to obtain the estimated signal.Some simulation examples are given for testing the performance of the proposed algorithm.With this multiscale analysis/synthesis design via the technique of the wavelet filter bank,the multiscale Wiener filter can be applied to treat the signal restoration problem from nonstationary 1/f fractal noise.1/f fractal noise was restrained effectively and the signal to noise is improved evidently.