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  • 图像非局部均值滤波的原理

      图像非局部均值滤波的原理和空间局部滤波不相同,局部空间滤波实质上是在频域上对图像进行滤波处理,而非局部均值滤波利用了噪声的非相关的特性。如下图所示,在一幅图像中,具有相同像素的图像块是很多的,而其中的噪声是不相关的。

    我们假设无噪声像素块为f(x,y),加性噪声为n(x,y),那么加噪后的像素块为g(x,y)=f(x,y)+n(x,y);我们把多个像素块进行叠加然后取平均值得到

    对该像素块取均值得到:

    由于像素块的相似性,上式中右边第一项化简为f(x,y),第二项由于噪声的均值为0,所以

    另外由于噪声的非相关性,在任意点(x,y)处的g(x,y)方差为

    所以,方差为:

    由此可见,通过非局部均值的方法可以减少图像中的噪声。

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   

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  • 原文地址:https://www.cnblogs.com/helloforworld/p/5303422.html
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