小波域Wiener滤波方法及其在功能磁共振成像中的应用

Application of Wiener filter based wavelet domain in functional magnetic resonance imaging

目的:探讨基于多分辨率分析理论的小波域Wiener滤波方法,并观察其在功能磁共振数据分析中的降噪效果。方法:①小波域Wiener滤波方法介绍:时间域高分辨率功能磁共振图像常常带有大量噪声,并且其分布是不确定的,基于多分辨率分析理论的小波域Wiener滤波将不确定分布的一般噪声转换到小波域相互正交的不同尺度空间上,使其在同一尺度空间上为互不相关的附加高斯分布。应用小波削弱算法Wiener滤波分别在不同尺度空间上进行降噪,同时对同一尺度空间信号使用了稳健中位数法进行估计。②应用该方法分别对模拟数据(一方波加上随机噪声,主要是模拟实际的功能磁共振方波)和真实数据进行分析及处理。结果:①模拟数据去噪前、后信噪比分别为68.987,78.529,表明降噪后信噪比明显提高;加噪声的混合数据、经小波处理后的数据与未加噪声的原数据很接近,附加的噪声得到了明显的抑制。②真实数据计算结果表明,经小波域Wiener滤波降噪以后,提高了数据的信噪比,从而能够更有效地提取信号,有助于识别新的有效激活区或排除伪激活区。结论:在功能磁共振数据分析中应用小波域Wiener滤波方法降噪是有效的。

AIM： To explore the method of Wiener filter incorporating wavelet domain using multi-resolution analysis, and investigate its denoising effect on functional Magnetic Resonance Imaging （fMRI）. METHODS： ①Introduction of Wiener filter based wavelet domain： MRI acquired with temporal high resolution often exhibits large noise artifacts. The distribution of temporal noises is uncertain in most cases. We transform the uncertainly distributed noises into the space with a series of orthonormal basis functions using different spatial scales, and analyze data using uncorrelated Gaussian distribution in the subspace of each spatial scale. The fMRI data can be de-noised in different spatial scales using wavelet shrinkage algorithm. In each spatial scale, the robust median method is used to approximate the signals. ②This method is also applied to analyze and process the analog data （square wave and random noise are combined to stimulate fMRI data） and the real data. RESULTS： ①The signal-to-noise ratio of fMRI data was obviously increased after denoising （68.987, 78.529）; The mixed data, wavelet-processed data and original data were identical, additional noise could be controlled. ②The experimental result of real data indicated that, the denoising using Wiener filter based wavelet domain could increase the signal-to-noise ratio of data and the effectiveness of extracting the signal, so as to discriminate the effective transactivation domain or eliminate false transactivation. CONCLUSION： Wiener filter based wavelet domain is effective on the denoising of fMRI data.