Résumé : We consider the monogenic representation for self-similar random fields. This approach is based on the monogenic representation of a greyscale image, using Riesz transform, and is particularly well-adapted to detect directionality of self-similar Gaussian fields. In particular, we focus on distributions of monogenic parameters defined as amplitude, orientation and phase of the spherical coordinates of the wavelet monogenic representation. This allows us to define estimators for some anisotropic fractional fields. We then consider the elliptical monogenic model to define vector-valued random fields according to natural colors, using the RGB color model. Joint work with Philippe Carre (XLIM, Poitiers), Céline Lacaux (LMA, Avignon) and Claire Launay (IDP, Tours).

Keywords : Gaussian random fields; self-similarity; monogenic signal