A linear image reconstruction framework based on sobolev type inner products

Authors:
Bart Janssen;Frans Kanters;Remco Duits;Luc Florack;Bart ter Haar Romeny
Affiliations:
Eindhoven University of Technology, Eindhoven, The Netherlands;Eindhoven University of Technology, Eindhoven, The Netherlands;Eindhoven University of Technology, Eindhoven, The Netherlands;Eindhoven University of Technology, Eindhoven, The Netherlands;Eindhoven University of Technology, Eindhoven, The Netherlands
Venue:
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Year:
2005

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Abstract

Exploration of information content of features that are present in images has led to the development of several reconstruction algorithms. These algorithms aim for a reconstruction from the features that is visually close to the image from which the features are extracted. Degrees of freedom that are not fixed by the constraints are disambiguated with the help of a so-called prior (i.e. a user defined model). We propose a linear reconstruction framework that generalises a previously proposed scheme. As an example we propose a specific prior and apply it to the reconstruction from singular point s. The reconstruction is visually more attractive and has a smaller $\mathbb{L}_{\rm 2}$-error than the previously proposed linear methods.