噪声密度不敏感的随机采样椒盐噪声滤波算法

中值滤波系列算法在处理被不同密度椒盐噪声污染的细节图像和平坦图像时，降噪性能不一致。本文借鉴开关中值滤波和压缩感知的思想，提出了随机采样滤波算法去除椒盐噪声。算法以噪声检测为基础，将被椒盐噪声污染的图像分为疑似噪声像素和信号像素，随机采样仅对信号像素采样。然后，利用正交匹配追踪算法重构出被污染前的图像，替代了中值滤波对噪声像素的估计。由于随机采样滤波基于压缩感知理论，对稀疏信号的重构具有最少测量次数的条件，因此随机采样点的数量具有一定的浮动空间，表现为对噪声密度不敏感。以被不同噪声密度污染图像的纹理、平坦局部区域进行验证，实验表明，当噪声密度在一定范围内变化时，算法可以实现对噪声密度不敏感。在高密度噪声污染的情况下，相较于中值滤波系列算法，随机采样滤波算法具有更好的细节保留能力和滤波能力。对标准测试图像进行了全局滤波，不同噪声密度具有一致的滤波效果，与自适应滤波算法相比，随机采样滤波算法在处理包含密集边缘特征的区域时更具备优势。 

Noise Density insensitive Random Sampling Salt and Pepper Filtering Algorithm

 Median filtering group algorithms have no consistent performance while deal with texture image and flat image with different salt and pepper noise densities. Referring to the idea of switching median filter and compressive sensing, we proposed a random sampling filtering algorithm to remove the salt and pepper noise. Based on noise detection, the polluted image is classified into noise pixels and signal pixels, which makes random sampling process could only sample signal pixels. Then Orthogonal Matching Pursuit method is used to recover original unpolluted image instead of estimating noise pixels with median filtering. Due to compressive sensing theory, there is a minimum measurement condition for sparse signal recovery. So the quantity of random sampling has domain of walker, which makes filtering results manifest noise density insensitive. We verified the algorithm with texture and flat area in image polluted by different salt and pepper noise densities. Simulation results showed that in a range of noise density, the random sampling filtering was noise density insensitive. And in high density noise condition, compared with median filtering group algorithms, our method has better performance in removing salt and pepper noise and preserving the details of image. The global filtering of the standard test image was carried out, and the results were consistent with the different noise densities. Compared with the adaptive filtering algorithm, the random sampling filtering algorithm has advantages in dealing with the regions with complex edge feature.