基于核主成分分析的图像去噪

简介了核主成分分析的原理及利用核主成分分析的图像去噪方法.通过使用核函数,在特征空间中对噪声图像使用主成分分析进行降噪处理.基于MDS的思想,使用核方法计算出在特征空间中降噪后的图像与其邻域点之间的内积约束关系,通过核函数重构出在原空间中降噪图像与其邻域点的内积约束关系,基于此内积约束关系在原空间中重构出降噪图像,从而达到通过核主成分分析对图像降噪的目的.比原有的MDS算法更稳定,对图像的噪声部分有更好的去除效果.

Image Denoising Based on Kernel Principal Component Analysis

In this paper, we address the principle of kernel principal component analysis and the problem of image denoising based on the kernel principal component analysis. At first, we process image denoising using principal component analysis in feature space. Based on MDS, we obtain inner product between the reconstructed point and its neighbors in the origin space through the dot product kernel function using the inner product between the reconstructed point and its neighborhood points in the feature space. And finally we reconstruct the pre-image in the origin space using this relationship of the inner product constraint. Compared with the original MDS, the algorithm of this paper gets better results on the image denoising and better stability. Keywords: kernel principal component analysis; kernel function; local linear reconstruction; coefficient of the projection.