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

Authors:
Sergio Amat;Rosa Donat;Jacques Liandrat;J. Carlos Trillo
Affiliations:
Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Spain;Departament de Matematica Aplicada, Universitat de Valencia, Spain;Ecole Generaliste d'Ingenieurs de Marseille (EGIM), Laboratoire d'Analyse Topologie et Probabilites (LATP), France;Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Spain
Venue:
Foundations of Computational Mathematics
Year:
2006

Citing 0
Cited 17

Error bounds for a convexity-preserving interpolation and its limit function

Journal of Computational and Applied Mathematics
Compression of color image using nonlinear multiresolutions

ISPRA'06 Proceedings of the 5th WSEAS International Conference on Signal Processing, Robotics and Automation
Point values Hermite multiresolution for non-smooth noisy signals II

ISPRA'06 Proceedings of the 5th WSEAS International Conference on Signal Processing, Robotics and Automation
A review on the piecewise polynomial harmonic interpolation

Applied Numerical Mathematics
Nonlinear Harten's multiresolution on the quincunx pyramid

Journal of Computational and Applied Mathematics
On a class of L1-stable nonlinear cell-average multiresolution schemes

Journal of Computational and Applied Mathematics
A family of stable nonlinear nonseparable multiresolution schemes in 2D

Journal of Computational and Applied Mathematics
Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms

Advances in Computational Mathematics
SVD-wavelet algorithm for image compression

MIV'05 Proceedings of the 5th WSEAS international conference on Multimedia, internet & video technologies
Weighted-powerp nonlinear subdivision schemes

Proceedings of the 7th international conference on Curves and Surfaces
On a (W)ENO-type multiscale representation based on quincunx refinement: application to image compression

Proceedings of the 7th international conference on Curves and Surfaces
Adaptive interpolation of images using a new nonlinear cell-average scheme

Mathematics and Computers in Simulation
A fully adaptive multiresolution scheme for image processing

Mathematical and Computer Modelling: An International Journal
Analysis of a class of nonlinear and non-separable multiscale representations

Numerical Algorithms
A class of nonlinear four-point subdivision schemes

Advances in Computational Mathematics
Nonlinear thresholding of multiresolution decompositions adapted to the presence of discontinuities

Advances in Computational Mathematics
High order nonlinear interpolatory reconstruction operators and associated multiresolution schemes

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

A nonlinear multiresolution scheme within Harten's framework is presented, based on a new nonlinear, centered piecewise polynomial interpolation technique. Analytical properties of the resulting subdivision scheme, such as convergence, smoothness, and stability, are studied. The stability and the compression properties of the associated multiresolution transform are demonstrated on several numerical experiments on images.