Iterative Kernel Principal Component Analysis for Image Modeling
K. I. Kim, Matthias Franz and Bernhard Schölkopf
IEEE Trans. PAMI
In recent years, Kernel Principal Component Analysis (KPCA) has been suggested for various image processing tasks requiring an image model such as, e.g., denoising or compression. The original form of KPCA, however, can be only applied to strongly restricted image classes due to the limited number of training examples that can be processed. We therefore propose a new iterative method for performing KPCA, the Kernel Hebbian Algorithm. By kernelizing the Generalized Hebbian Algorithm, one can iteratively estimate the Kernel Principal Components with only linear order memory complexity. In our experiments, we compute models for complex image classes such as faces and natural images which require a large number of training examples. The resulting image models are tested in single-frame super-resolution and denoising applications. Although the KPCA model is not specifically tailored to these tasks, both super-resolution and denoising performance are comparable to existing methods. The same model can be used in tasks with variable inputs, for instance super-resolution with variable input resolution, or denoising with unknown noise characteristics.