Bayesian estimation of the multifractality parameter for images via a closed-form Whittle likelihood

Sebastien Combrexelle, Herwig Wendt, Jean-Yves Tourneret, Patrice Abry, Stephen McLaughlin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)


Texture analysis is central in many image processing problems. It can be conducted by studying the local regularity fluctuations of image amplitudes, and multifractal analysis provides a theoretical and practical framework for such a characterization. Yet, due to the non Gaussian nature and intricate dependence structure of multifractal models, accurate parameter estimation is challenging: standard estimators yield modest performance, and alternative (semi-)parametric estimators exhibit prohibitive computational cost for large images. This present contribution addresses these difficulties and proposes a Bayesian procedure for the estimation of the multifractality parameter c2 for images. It relies on a recently proposed semi-parametric model for the multivariate statistics of log-wavelet leaders and on a Whittle approximation that enables its numerical evaluation. The key result is a closed-form expression for the Whittle likelihood. Numerical simulations indicate the excellent performance of the method, significantly improving estimation performance over standard estimators and computational efficiency over previously proposed Bayesian estimators.

Original languageEnglish
Title of host publication2015 23rd European Signal Processing Conference (EUSIPCO)
Number of pages5
ISBN (Print)9780992862633
Publication statusPublished - 2015
Event23rd European Signal Processing Conference 2015 - Nice, France
Duration: 31 Aug 20154 Sept 2015


Conference23rd European Signal Processing Conference 2015
Abbreviated titleEUSIPCO 2015


  • Bayesian estimation
  • Hankel transform
  • Multifractal analysis
  • Texture analysis
  • Whittle likelihood

ASJC Scopus subject areas

  • Media Technology
  • Computer Vision and Pattern Recognition
  • Signal Processing


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