Face Hallucination Through KPCA
This paper demonstrates how Kernel Principal Component Analysis (KPCA) can be used for face hallucination. Different with other KPCA-based methods, KPCA in this paper handles samples from two subspaces, namely the high- and low- resolution image spaces. As KPCA learns not only linear features but also non-linear features, it is anticipated that more detailed facial features could be synthesized. We propose a new model and give theoretical analysis on when it is applicable. Algorithm is then developed for implementation. Experiments are conducted to compare the proposed method with the existing well-known face hallucination methods in terms of visual quality and mean square error. Our results are better and encouraging. Motivated by Wang and Tang's (2) work and the successful applications of KPCA for other face image preprocessing (10)(12), we develop a new method to learn both linear and non-linear intrinsic properties of low-resolution image and high-resolution image using KPCA. Unlike PCA, KPCA is nonlinear and can model structures in given data set better, so that more detailed features could be synthesized. However, we would analyze in next section that the KPCA-based method can not be developed in a straightforward way just by simple combination of kernel and the PCA-based method. As will be analyzed later, the main difficulty is that it is generally difficult to find the relationship between the two kernel feature spaces corresponding to low- and high- resolution data respectively, while the assumption used in PCA-based face hallucination cannot be applied for kernel approach. In order to solve such problem, we propose a new model by assuming that when suitable kernels are used, different resolution images can approximately have the same intrinsic features in their corresponding kernel principal subspaces. Theoretical analysis why this assumption can be applicable will be given. Following this model, the KPCA-based face hallucination method is then developed. In addition, we also propose a new two-step face hallucination approach by integrating the residue compensation to enhance the equality of reconstructed high- resolution images.