在此基础上，分析了一些非线性滤波的改进算法，根据这些改进算法，提出了新的数字图像非线性滤波改 进算法：首先，在加权和多级中值滤波算法的基础上，提出了多级非线性加权平均中值滤波改进算法，通 过对滤波窗四个子集中加入滤波点周围最近的四个像素，强化了滤波点及其周围的像素，突出了滤波点及 其周围像素点在计算中值时的作用，使输出中值更接近于原始点像素；其次，根据几种阈值中值滤波算法， 结合粗糙集理论，提出了基于粗糙集理论的图像中值滤波改进算法，该算法通过对滤波窗的均值与滤波点 像素的差和设定阈值进行比较，按粗糙集理论对比较结果进行分类，使图像分为噪声和信号两类，然后只 对噪声滤波，减少了图像的模糊，保持了图像的细节；最后，根据数学形态学的膨胀、腐蚀、开和闭等运 算能保护图像边缘的特性，提出了非线性滤波的数学形态改进算法，该算法对含噪图像先闭运算，再开运 算，并把运算后两图像之差中值滤波，滤波后再加回开运算的图像，该算法减少了闭、开运算对图像信号 的损失，保持了图像细节。通过对滤波后图像的一些客观指标 (峰值信噪比、归一化均方误差、归一化平 均绝对误差)的比较，证明本文算法优于以前的改进算法。

This paper simply introduces the emergence, development, basic working theory and characteristics of nonlinear filter—median filter. Based on these, some improved algorithms of nonlinear filter have been analyzed, according to these, some new improved algorithms of nonlinear filter have been presented in digital image: In the first place, improved multilevel nonlinear weighted mean median filter algorithm has been presented based on weighted and multilevel median filter via joined the nearest four pixels of filter dot in the four filter windows subclass, strengthening the pixels of filter dot as well as its surrounding, stand out the effect of calculating median in the pixels of filter dot as well as its surrounding, making export median close to originality pixel dot even more; Secondly ,an image median filter based on Rough Sets theory has been presented according to several threshold value algorithms of median filter and Rough Sets theory. Via comparing to the contrast between enactment threshold value and the difference of mean value of the filter window and filter dot pixel, applying to the compared result of Rough Sets theory, the image has classified the two kinds of the noise and signal, then noises have only been filtered and reduced the blur of image and held the image detail; Finally, according to the trait that dilation, erosion, opening and closing etc. operation of mathematics morphology can protect image edge, mathematics morphology improved algorithm of nonlinear filter has presented. This algorithm makes the opening operation to the noised image firstly, then closing operation, and does median filter to the difference of the two images operated, after filtered, adds the image to the image of opening operation. This algorithm reduces the image signal loss of the closing and opening operation and keeps the image detail. It has been proved that this algorithm is better than these former algorithms through the contrast of image impersonality criterion (peak signal to noise ratio, normalized mean square error, normalized mean absolute error).