H ö Lderian Regularity-Based Image Interpolation

We consider the problem of interpolating a signal in R^d known at a given resolution. In our approach, the signal is assumed to belong to a given (large) class of signals. This class is characterised by local regularity constraints, that can be described by a certain inter-scale behaviour of their wavelet coefficients. These constraints allow to predict the scale n coefficient from the ones at lower scales. We investigate some properties of this interpolation scheme. In particular, we give the Holder regularity of the refined signal, and present some asymptotic properties of the method. Finally, numerical experiments are presented. Both the theoretical and numerical results show that our regularity-based scheme allows to obtain good quality interpolated images