IMAGE INTERPOLATION BASED ON VARIATIONAL-PRINCIPLES

This paper presents a new image interpolation approach based on variational principles. The image interpolation problem is formulated as the constrained minimization of a certain functional. The choice of the functional to be minimized is based on the combination of the restrictions imposed by the mathematical problem and certain considerations related to the physical problem. This paper focuses on the class of nonnegative quadratic functionals whose minimization amounts to 2-D L-generalized splines. The partial differential operators used correspond to certain stochastic partial differential equation (SPDE) image models. Image interpolation is exactly formulated in its discrete form and an extensive analytical treatment of the resulting minimization problem is subsequently presented. The implementation difficulties and computational requirements indicate that such a formulation cannot provide interpolation algorithms of practical value. The derivation of practical interpolation algorithms is based on an alternative formulation of the optimization problem. This new formulation allows the transformation of the original constrained minimization into an equivalent unconstrained one. A number of interpolation algorithms is proposed, based on various noncausal and semicausal SPDE image models. Finally, experimental results are presented, compared and discussed.