Basarab Matei

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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 propose to improve the classical lifting-based wavelet transforms by defining three classes of pixels which will be predicted differently. More specifically, the proposed idea is inspired by the Essentially Non-Oscillatory (ENO) transform and consists in shifting the stencil used for prediction in order to reduce the error near image(More)
The aim of this paper is to construct a new nonlinear and nonseparable multiscale representation of piecewise continuous bidimensional functions. This representation is based on the definition of a linear projection and a nonlinear prediction operator, which locally adapts to the function to be represented. This adaptivity of the prediction operator proves(More)