基于马氏距离的改进非局部均值图像去噪算法

摘要

An improved non-local means (NLM) image denoising algorithm is proposed, which uses Mahal-anobis distance to measure the similarity between the image pixels. Firstly, calculating the Mahalanobis dis-tance between the image pixels in the eigenspace since the Mahalanobis distance is not robust in the sample space. Secondly, the image data is analyzed with the principal component analysis method, thus the Maha-lanobis distance equation is simplified. Finally, the improved NLM image denoising algorithm is obtained with the Gaussian weighted kernel function which is composed of the simplified Mahalanobis distance. The experimental results on several typical images show that the improved NLM algorithm can achieve better denoising effect than the original NLM algorithm with a variety of image quality evaluation method. The filter parameter ‘h’ in the improved NLM denoising algorithm is analyzed in details and the equation be-tween the filter parameter ‘h’ and the image noise variance is estimated. Based on the equation, the experi-mental results achieve nearly best denoising performance of the improved filtering algorithm.%通过对原非局部均值(NLM)图像去噪算法进行改进，提出一种利用马氏距离作为衡量图像像素点相似性的非局部均值图像去噪算法。首先针对样本空间中马氏距离不稳定的特点计算特征空间中的马氏距离；然后对图像数据进行相关性分析和降维处理，提取数据主成分，简化特征空间中马氏距离的计算方法；最后利用此马氏距离生成高斯加权核函数，对图像进行去噪。采用一系列加有噪声的典型图像对文中算法进行实验，证明了该算法可获得比原NLM图像去噪算法更好的去噪效果；利用多组数据对文中算法中的滤波参数h进行分析，得到噪声方差与滤波参数h的关系式，可以获得接近于改进图像去噪算法的最佳去噪性能。