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Anisotropic phenomena can be observed almost everywhere in nature. This makes them important subjects for theoretical and experimental studies. In this work, we focus on the study of anisotropic quasi-self-similar signals. It holds that the classical multifractal formalism in all its formulations does not hold for this class. We then use an homogeneous norm introduced by Calderon and Torchinsky to check the validity of an adapted anisotropic multifractal formalism for these signals. Our techniques are based on group theory combined with wavelet characterization of anisotropic function spaces. We then show the efficiency of anisotropic wavelets in detecting singularities.

An adapted group-dilation anisotropic multifractal formalism for functions