Wavelet Leader based Multifractal Analysis

We introduce a new multifractal formalism based on wavelet leaders and study its properties. Comparing it against previously formulated wavelet coefficient based multifractal formalism, we show first that this wavelet leader based formalism allows the multifractal spectrum to be obtained over its entire range, and second that it does not cease to hold when applied to processes embodying unusual chirp-type (or oscillating) singularities (as opposed to the more common cusp-type ones). We illustrate these results and properties on four examples of multifractal deterministic functions or stochastic processes containing a graduation of the major difficulties. We show that this new multifractal formalism benefits from excellent theoretical and practical performance. Matlab routines implementing it are available upon request.