关键词: 巴特沃斯滤波器, 频率域, 直方图, 信噪比

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