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This paper introduces and analyzes new approximation procedures for bi-variate functions. These procedures are based on an edge-adapted nonlinear reconstruction technique which is an intrinsically two-dimensional extension of the essentially non-oscillatory and subcell resolution techniques introduced in the one dimensional setting by Harten and Osher.(More)
We study in this paper nonlinear subdivision schemes in a multivariate setting allowing arbitrary dilation matrix. We investigate the convergence of such iterative process to some limit function. Our analysis is based on some conditions on the contractivity of the associated scheme for the differences. In particular, we show the regularity of the limit(More)
The aim of the paper is the construction and the analysis of nonlinear and non-separable multi-scale representations for multivariate functions. The proposed multi-scale representation is associated with a non-diagonal dilation matrix M. We show that the smoothness of a function can be characterized by the rate of decay of its multi-scale coefficients. We(More)
In this paper, we introduce a particular class of nonlinear and non-separable multiscale representations which embeds most of these representations. After motivating the introduction of such a class on one-dimensional examples, we investigate the multi-dimensional and non-separable case where the scaling factor is given by a non-diagonal dilation matrix M.(More)