中文摘要：

目的：评估一种新的正电子发射断层扫描技术（PET）图像去噪方法—非局部几何非线性扩散滤波。方法：首先,计算PET图像的几何非线性扩散系数;然后,对该扩散系数进行非局部邻域加权平均;最后,用非局部加权平均后的扩散系数对PET图像进行几何非线性扩散滤波。结果：与原几何非线性扩散滤波、非局部均值滤波、PURE-LET滤波方法相比,非局部几何非线性扩散滤波可提高PET图像峰值信噪比和结构相似性,增强图像视觉效果。结论：非局部几何非线性扩散滤波是一种有效的PET图像去噪方法。

英文摘要：

Objective To assess a novel non-local geometric nonlinear diffusion filter for denoising positron emission tomography（PET） images. Methods The geometric nonlinear diffusion coefficients of PET images were firstly calculated. And then, the nonlocal weighted average of the calculated coefficients was taken. Finally, the diffusion coefficients after the non-local geometric weighted averaging were applied for the geometric nonlinear diffusion filtering（GNLDF）. Results Compared with GNLDF, nonlocal mean filtering and PURE-LET filtering, the non-local GNLDF improved the peak signal-to-noise ratio and structural similarity of PET images, and enhanced the image visual effect. Conclusion The non-local GNLDF is an efficient method for denoising PET image.