Research Of Image Denoising Methods Based On Kernel Principal Component Analysis

This paper studies the problem of image denoising based on kernel principal component analysis. The method of kernel principal component analysis of image denoising is a noise reduction technology based on machine learning appeared in recent years. Considering the nonlinear image information and the principal component of image dispersed in the original space, while the kernel principal component analysis using the kernel method to extract the nonlinear principal component of the image through the nonlinear transformation mapping the image to the feature space to denoise, the effect of noise reduction is much better than that of principal component analysis.Based on deep research about technology of denoising using kernel principal component analysis, we do the following three aspects in this paper due to the disadvantage of instability and easy to fall into local minimum of traditional iterative algorithm and the defect of high computational complexity caused by amounts of distance computation in multidimensional scale method.Firstly, based on the idea of preserving neighborhood relationship in multidimensional scale method, this paper reduce noise through extracting nonlinear principal component of noisy pattern in feature space by using kernel function. And using kernel method, we compute the relationship between denoised pattern and its neighborhood in feature space. Then we reconstruct the relationship between denoised pattern and its neighborhood in original space through the relationship between denoised pattern and its neighborhood in feature space by using constructed kernel function. Finally we reconstruct the denoised pattern using this relationship between denoised pattern and its neighborhood in original space. Because our method involves only linear algebra, it can avoid the disadvantage of instability and easy to fall into local minimum of traditional iterative algorithm.Secondly, this paper proposes the algorithm based on multidimensional inner product. We reconstruct denoised pattern through the inner product relationship accomplished by kernel method. Because of our method based on inner product, it avoids the instability caused by amounts of distance computation in multidimensional scales method, reduces the computational complexity and improves computing efficiency.Thirdly, we verify the effectiveness of the proposed algorithm through the numerical experiments and present our method to be more effective to improve the SNR of the image by comparing sophisticated algorithm results.