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- Albert Cohen, Basarab Matei
- ICIP
- 2001

This paper introduces and analyzes new approximation procedures for bivariate 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)

- Albert Cohen, Basarab Matei
- Tutorials on Multiresolution in Geometric…
- 2002

- Francesc Aràndiga, Albert Cohen, Manuel Doblas, Basarab Matei
- ICIP
- 2003

We introduce nonlinear edge-adapted multiresolution transforms for image processing. These transforms have the same structure as wavelet basis decompositions, but incorporate a specific geometric treatment of edges, which results in sparser representations of piecewise smooth images and in turn better compression properties. We also observe visual… (More)

- Basarab Matei, Sylvain Meignen, Anastasia Zakharova
- Asymptotic Analysis
- 2011

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)

- Basarab Matei, Sylvain Meignen, Anastasia Zakharova
- Journal of Approximation Theory
- 2011

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)

- Francesc Aràndiga, Albert Cohen, Rosa Donat, Basarab Matei
- Image Vision Comput.
- 2010

- Basarab Matei, Sylvain Meignen
- IEEE Transactions on Image Processing
- 2015

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)

- Basarab Matei, Sylvain Meignen
- Numerical Algorithms
- 2011

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)

We study the relationship between stable sampling sequences for bandlimited functions in Lp(Rn) and the Fourier multipliers in Lp. In the case that the sequence is a lattice and the spectrum is a fundamental domain for the lattice the connection is complete. In the case of irregular sequences there is still a partial relationship. 2010 Mathematics Subject… (More)