Many examples of signals and images cannot be modeled by locally bounded functions, so that the standard multifractal analysis, based on the H\"older exponent, is not feasible. We present a multifractal analysis based on another quantity, the p-exponent, which can take arbitrarily large negative values. We investigate some mathematical properties of this exponent, and show how it allows us to model the idea of "lacunarity" of a singularity at a point. We finally adapt the wavelet based multifractal analysis in this setting, and we give applications to a simple mathematical model of multifractal processes: Lacunary wavelet series.
@article{arxiv.1505.06885,
title = {Multifractal analysis based on p-exponents and lacunarity exponents},
author = {Patrice Abry and Stéphane Jaffard and Roberto Leonarduzzi and Clothilde Melot and Herwig Wendt},
journal= {arXiv preprint arXiv:1505.06885},
year = {2015}
}