Multifractal analysis based on p-exponents and lacunarity exponents
Patrice Abry, Stéphane Jaffard, Roberto Leonarduzzi, Clothilde Mélot, Herwig Wendt · arXiv (Cornell University) · 2015
Many examples of signals and images cannot be modeled by locally bounded functions, so that the standard multifractal analysis, based on the Hölder 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.