De-noising and Recovering Images Based on Kernel PCA Theory

Pengcheng Xi, Tao Xu
Nanjing Univ. of Aeronautics & Astronautics
College of Information Science and Technology
210016, Nanjing
P.R. of China



Principal component analysis (PCA) is a basis transformation to diagonalize an estimate of the covariance matrix of the input data. And the new coordinates in the Eigenvector basis, are called principal components. Since Kernel PCA is nothing but a PCA in feature space , the projection of an image in input space can be constructed from its principal components in feature space. This paper starts with relational theories concerning kernel and principal component extraction. Then the focus is converged onto de-noising and recovering images (i.e. finding the exact or approximate pre-image of a noised and deformed one in an example database).

To make the above theories and applications persuasive, several experiments on both binary and gray images are delivered here, which include finding pre-images (exact or approximate) based on a small database composed of one Chinese character of different fonts, and another database of similar gray images of various gray-scale distributions. Through the experiments using Kernel PCA methods, we find our method performs well in solving above problems. Compared with the performance using linear PCA, our method also out-performs for its distinguished quality and practicality.

Keywords: Kernel; Principal component extraction; Feature space; De-noising and recovering