On the Role of Exponential Functions in Image Interpolation
Hagai Kirshner, Department of Electrical Engineering, Technion, Israel

Seminar • 22 October 2008 • BM 5.202

Abstract
A reproducing-kernel Hilbert space approach to image interpolation is introduced. In particular, the reproducing kernels of Sobolev spaces are shown to be exponential functions. These functions, in turn, give rise to interpolation kernels that outperform presently available methods. Both theoretical and experimental results are presented. A tight l_2 upper-bound on the interpolation error is then derived, indicating that the proposed exponential functions are optimal in this regard. Furthermore, a unified approach to image interpolation by ideal and non-ideal sampling procedures is derived and demonstrated, suggesting that the proposed exponential kernels may have a significant role in image modeling as well. Our conclusion is that the proposed Sobolev-based approach could be instrumental and a preferred alternative in many interpolation tasks.