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。

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               

posted @ 2016-03-21 20:02  helloforworld  阅读(9426)  评论(0编辑  收藏  举报