Some physical phenomena like diffusion limited aggregates and fully developed turbulence seem to exhibit some kind of self similarity. The validity of the multifractal formalism via the H�lder regularity has been proved to hold for self-similar signals or functions but it fails for non isotropic self-similar functions because in general context, non isotropic signals do not propagate in a fixed direction but in contrast they can present some deformations. We introduce then two approaches for the spectrum of singularity which take into account the behavior of non isotropic signals and the directions of propagation. These spectra induce a new approach of the multifractal formalism. We check the validity of such a formalism for the class of non isotropic quasi-self-similar signals.

wavelets, self-similarity, multifractal analysis, regularity, multifractal formalism.