On a nonlinear mean and its application to image compression using multiresolution schemes

Abstract

This paper is devoted to the compression of colour images using a new nonlinear cell-average multiresolution scheme. The aim is to obtain similar compression properties as linear multiresolution schemes but eliminating the classical Gibbs phenomenon of this type of reconstructions near the edges. The algorithm is based on a nonlinear reconstruction operator (using a nonlinear trigonometric mean). The new reconstruction is third-order accurate in smooth regions and adapted to the presence of discontinuities. The data used are always centred with optimal support. Some theoretical properties of this scheme are analysed (order of approximation, convergence, elimination of Gibbs effect and stability).