Directionlets and Some Generalized Nonlinear Selfsimilarities
Anouar Ben Mabrouk · 2011
In this paper we review the notion of directional regularity and we introduce quite equivalent definitions using polar systems. Next, we prove a wavelet characterization of such regularities with directional wavelets known as directionlets. A class of nonlinear anisotropic self similar functions is then introduced and proved to be compatible with directionlets for the detection of the singularities. At the end, we propose some prospects to be adapted for the study of spherical detected signals. Mathematics Subject Classification: 42C40, 28A80, 76M55