Abstract: In order to eliminate salt-and-pepper noise that exists in the digital image collection and processing，an improved filtering algorithm with accurate noise pixels detection in GF（2⁸） finite field is presented.According to the correlativity of adjacent pixels this paper proposes the pixel similarity function in GF（2⁸） field.Based on it，image salt-and-pepper noise self-adaptive detector is given.It can detect noise accurately.And then the digital image salt-and-pepper noise self-adaptive filtering is completed combined with median filtering.Simulation results show that this algorithm is accurate on noise detection.And this algorithm is better than other algorithms at filtering salt and pepper noise and preserving the detail of image.And the restoring effect of image is good under high noisy rate.

Key words: noise detection, GF（2⁸） finite field, correlativity of pixels, similarity function, median filtering

摘要： 针对数字图像采集及处理过程中广泛存在的椒盐噪声，基于GF（2⁸）有限域，提出一种具有噪声点精确检测能力的改进型噪声滤波算法。根据图像相邻像素相关性，构建了GF（2⁸）域上的相似函数，并据此提出了GF（2⁸）域上的图像自适应椒盐噪声检测算子，可对噪声点准确定位；结合中值滤波算法完成数字图像的椒盐噪声自适应滤除。实验表明提出算法对噪声点定位准确，在图像的恢复和保护图像细节方面对比其他算法有较大提高，对强噪声污染图像的恢复也有较好效果。

关键词: 椒盐噪声, 噪声检测, GF（2⁸）域, 像素相关性, 相似函数, 中值滤波