English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Multifractal analysis has become a powerful signal processing tool thatcharacterizes signals or images via the fluctuations of their pointwiseregularity, quantified theoretically by the so-called multifractal spectrum.The practical estimation of the multifractal spectrum fundamentally relies onexploiting the scale dependence of statistical properties of appropriatemultiscale quantities, such as wavelet leaders, that can be robustly computedfrom discrete data. Despite successes of multifractal analysis in variousreal-world applications, current estimation procedures remain essentiallylimited to providing concave upper-bound estimates, while there is a priori noreason for the multifractal spectrum to be a concave function. This workaddresses this severe practical limitation and proposes a novel formalism formultifractal analysis that enables nonconcave multifractal spectra to beestimated in a stable way. The key contributions reside in the development andtheoretical study of a generalized multifractal formalism to assess themultiscale statistics of wavelet leaders, and in devising a practical algorithmthat permits this formalism to be applied to real-world data, allowing for theestimation of nonconcave multifractal spectra. Numerical experiments areconducted on several synthetic multifractal processes as well as on areal-world remote-sensing image and demonstrate the benefits of the proposedmultifractal formalism over the state of the art.

A Generalized Multifractal Formalism for the Estimation of Nonconcave Multifractal Spectra