Abstract: For the shortcomings of the traditional filter in the noise detection and filtering, this paper presents a new noise detection method and inverse harmonic mean filtering algorithm based on quotient space granular computing theory. The image with noise is divided into hierarchical granularity to form a semi order quotient space lattice, and then according to principle of falsity preserving, the proper granularity space is selected to classify the noise into two classes and it is filtered respectively. The experimental results show that the algorithm can filter out the noise better while keeping the details of the image texture features, improving image quality, and increasing signal to noise ratio.

Key words: quotient space theory, granularity, noise detection, granular-inverse harmonic mean filter

摘要： 针对传统滤波器在噪声检测和滤除中存在的不足，提出了基于商空间粒度理论的噪声检测和粒度逆谐波均值滤波算法。该算法将受噪声污染的图像划分成不同粒度层次的商空间，形成商空间半序格，结合保假原理选择适当的粒度空间实施噪声分类检测和分别滤除。实验结果表明，该算法在滤除噪声的同时能够较好地保持图像的细节纹理特征、改善图像质量、提高信噪比等。

关键词: 商空间理论, 粒度, 噪声检测, 粒度逆谐波均值滤波