On a nonlinear cell-average multiresolution scheme for image compression

Resumen

The aim of this paper is to present a new nonlinear cell-average multiresolution scheme and its application to the compression of color images. The objective is to obtain an algorithm competing with linear multiresolution transforms in smooth regions but exhibiting a better behaviour (compression, Gibbs phenomenon reduction, . . .) in nonsmooth regions. Several desirable features can be associated to this new algorithm: the reconstruction operator is third-order accurate in smooth regions, the stencil used is always centred with optimal support and it is adapted to the presence of discontinuities. Monotony preservation, order of approximation, convergence of the associated subdivision scheme, elimination of Gibbs effects and stability are analysed. This paper can be considered as the second part of the paper by Amat, Donat, Liandrat and Trillo [ Foundations of Computational Mathematics, 6 (2), 193-225, (2006)] where the point-value framework was considered.