Distance based kernel PCA image reconstruction

Principal component analysis (PCA) is widely used in data compression, de-noising and reconstruction, but it is inadequate to describe real images with complex nonlinear variations, such as illumination, distortion, etc., because it is a linear method in nature. In this paper, kernel PCA (KPCA) is presented to describe real images, which combines the nonlinear kernel trick with PCA. First, the kernel trick is used to map the input data into an implicit feature space F, and then PCA is performed in F to produce nonlinear principal components of the input data. However, there exists a problem for KPCA reconstruction, as the feature space F is implicit and unknown. In order to deal with this problem, we propose to employ a new kernel called the distance kernel to set up a corresponding relation based on distance between the input space and the implicit feature space F. Experimental results illustrate that the proposed method has an encouraging performance.