Paris Dauphine University

About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Context (language use) & Population. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

Total variation based interpolation

Abstract: We propose an reversible interpolation method for signals or images, in the sense that the original image can be deduced from its interpolation by a sub-sampling. This imposes some constraints on the Fourier coefficients of the interpolated image. Now, there still exist many possible interpolations that satisfy these constraints. The zero-padding method is one of them, but gives very oscillatory images. We propose to choose among all possibilities, the one which is the most "regular". We justify the total variation of the image as a good candidate as measure of regularity. This yields to minimise a regularisation functional defined in space domain, with a constraint defined in the frequency domain.

Convergent difference schemes for nonlinear parabolic equations and mean curvature motion

Abstract: Explicit finite difference schemes are given for a collection of parabolic equations which may have all of the following complex features: degeneracy, quasilinearity, full nonlinearity, and singularities. In particular, the equation of “motion by mean curvature” is included. The schemes are monotone and consistent, so that convergence is guaranteed by the general theory of approximation of viscosity solutions of fully nonlinear problems. In addition, an intriguing new type of nonlocal problem is analyzed which is related to the schemes, and another very different sort of approximation is presented as well.