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Are polynomial models optimal for image interpolation?

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 that give rise to alternative interpolation kernels. Both theoretical and experimental results are presented, indicating that the proposed exponential functions perform better in terms of SNR and of boundary-effects removal than currently available methods, in particular polynomial-based kernels, while introducing no additional computational overhead.