On the Role of Exponential Splines in Image Interpolation

Hagai Kirshner and Moshe Porat,
Department of Electrical Engineering, 
Technion - Israel Institute of Technology 
Haifa 32000, Israel


Abstract

A Sobolev reproducing-kernel Hilbert space approach to image 
interpolation is introduced. The underlying kernels are exponential 
functions and are related to stochastic autoregressive image modeling. 
The corresponding image interpolants can be implemented effectively 
using compactly-supported exponential B-splines. A tight $\lebesgue$ 
upper-bound on the interpolation error is then derived, suggesting 
that the proposed exponential functions are optimal in this regard. 
Experimental results indicate that the proposed interpolation approach 
with properly-tuned, signal-dependent weights outperforms currently 
available polynomial B-spline models of comparable order. Furthermore, 
a unified approach to image interpolation by ideal and non-ideal 
sampling procedures is derived, 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.


IEEE Trans. on Image Processing,
vol. 18, no.10, pp. 2198-2208 (2009).