Analysis of a class of nonlinear and non-separable multiscale representations

Authors:
Basarab Mateï;Sylvain Meignen
Affiliations:
LAGA Laboratory, Paris XIII University, Villetaneuse, France;LJK Laboratory, University of Grenoble, Grenoble, France
Venue:
Numerical Algorithms
Year:
2012

Citing 11
Cited 0

Nonlinear pyramid transforms based on median-interpolation

SIAM Journal on Mathematical Analysis
Power ENO methods: a fifth-order accurate weighted power ENO method

Journal of Computational Physics
Analysis of a New Nonlinear Subdivision Scheme. Applications in Image Processing

Foundations of Computational Mathematics
A family of stable nonlinear nonseparable multiresolution schemes in 2D

Journal of Computational and Applied Mathematics
Full length article: Smoothness characterization and stability of nonlinear and non-separable multiscale representations

Journal of Approximation Theory
A 4-point interpolatory subdivision scheme for curve design

Computer Aided Geometric Design
Optimal biorthogonal wavelet decomposition of wire-frame meshes using box splines, and its application to the hierarchical coding of 3-D surfaces

IEEE Transactions on Image Processing
Hierarchical representation and coding of surfaces using 3-D polygon meshes

IEEE Transactions on Image Processing
The curvelet transform for image denoising

IEEE Transactions on Image Processing
Sparse geometric image representations with bandelets

IEEE Transactions on Image Processing
Oriented Wavelet Transform for Image Compression and Denoising

IEEE Transactions on Image Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

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. We also propose new convergence and stability results in L p and Besov spaces for that class of nonlinear and non-separable multiscale representations. We end the paper with an application of the proposed study to the convergence and the stability of some nonlinear multiscale representations.