We consider the problem of image interpolation using adaptive optimal recovery. We adaptively estimate the local quadratic signal class of our image pixels. We then use optimal recovery to estimate the missing local samples based on this quadratic signal class. This approach tends preserve edges, interpolating along edges and not across them.

We consider the problem of Lagrange polynomial interpolation in high or countably infinite dimension, motivated by the fast computation of solution to parametric/stochastic PDE’s. In such applications there is a substantial advantage in considering polynomial spaces that are sparse and anisotropic with respect to the different parametric variables. In an adaptive context, the polynomial space i...

The paper develops a semi-Lagrangian method for the numerical integration of the transport equation discretized on adaptive Cartesian cubic meshes. We use dynamically adaptive graded Cartesian grids. They allows for a fast grid reconstruction in the course of numerical integration. The suggested semi-Lagrangian method uses a higher order interpolation with a limiting strategy and a back-and-for...

The adaptive partition of unity interpolation method, introduced by Aiton and Driscoll, using Chebyshev local interpolants, is explored for interpolating functions with sharp gradients representing two-medium problems. For that evolve under vector fields, the patches (covers) can be shifted resized to follow changing dynamics profiles. method tested selected 1D 2D problems linear divergence-fre...

A 3D display using super high-density multiview images should enable reproduction of natural stereoscopic views. In the super multi-view display system, viewpoints are sampled at an interval narrower than the diameter of the pupil of a person’s eye. With the parallax produced by a single eye, this system can pull out the accommodation of an eye to an object image. We are now working on a real-t...