The a-priori information required for function approximation corresponds to an infinite number of data. The paper discusses template functions as example of an explicit implementation of infinite data. An infinite number of data can be empirically measured by a-posteriori control. While in classical convex regularization functionals template functions representing infinite number of data can be chosen identically zero, general non-convex a-priori information requires explicitly non-zero template functions.
Acknowledgements The author was supported by a Postdoctoral Fellowship (Le 1014/1-1) from the Deutsche Forschungsgemeinschaft and a NSF/CISE Postdoctoral Fellowship at the Massachusetts Institute of Technology. He also wants to thank Federico Girosi, Tomaso Poggio, Jörg Uhlig, Achim Weiguny, and Chris Williams for discussions.