Abstract: This paper describes a kind of mixed non-linear Butterworth filter based on the detailed analysis of the Butterworth low pass filter and that of the Butterworth high pass filter，and also，experiments are executed separately using these three types of filter to verify the intuitive validity of them.Besides，the criterion of Signal-to-Noise Rate SNR and signal-to-noise improving factor R are implied in the experiments in which the images are mixed with Gaussian，salt & pepper，speckle noises to compare the filtering effects of them from the view of statistics.The results show that the mixed non-linear Butterworth filter can depress the noise，maintain the details of the image，and it takes both the merits of Butterworth low-pass filter and high-pass filter，and also，the calculation is not complex，and therefore it turns out to be an active method to be realized.

Key words: Butterworth filter, frequency domain, histogram, signal-to-noise rate

摘要： 在详细分析频率域Butterworth低通、高通滤波器构造的基础上，提出一种基于Butterworth低通、高通滤波器基础上的非线性混合滤波器图像滤波方法，并利用Matlab软件对这3种滤波器进行了对比实验，从直观上进行了算法验证。此外，还采用信噪比SNR、信噪比改善因子R指标，分别利用这3种滤波器对加入高斯噪声、椒盐噪声和随机噪声的图像进行对比实验，从统计学角度再次进行算法验证。实验结果表明，这种非线性滤波器可以在滤除加性噪声的同时，保留图像细节，具备Butterworth低通、高通滤波器各自的优点，同时该滤波器计算也不太复杂，是一种易于实现的有效方法。

关键词: 巴特沃斯滤波器, 频率域, 直方图, 信噪比