Bayesian multifractal analysis of multi-temporal images using smooth priors

Sebastien Combrexelle, Herwig Wendt, Jean Yves Toumeret, Patrice Abry, Stephen McLaughlin

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

1 Citation (Scopus)


Texture analysis can be conducted within the mathematical framework of multifractal analysis (MFA) via the study of the regularity fluctuations of image amplitudes. Successfully used in various applications, however MFA remains limited to the independent analysis of single images while, in an increasing number of applications, data are multi-temporal. The present contribution addresses this limitation and introduces a Bayesian framework that enables the joint estimation of multifractal parameters for multi-temporal images. It builds on a recently proposed Gaussian model for wavelet leaders parameterized by the multifractal attributes of interest. A joint Bayesian model is formulated by assigning a Gaussian prior to the second derivatives of time evolution of the multifractal attributes associated with multi-temporal images. This Gaussian prior ensures that the multifractal parameters have a smooth temporal evolution. The associated Bayesian estimators are then approximated using a Hamiltonian Monte-Carlo algorithm. The benefits of the proposed procedure are illustrated on synthetic data.

Original languageEnglish
Title of host publication2016 IEEE Statistical Signal Processing Workshop (SSP)
ISBN (Electronic)9781467378024
Publication statusPublished - 25 Aug 2016
Event19th IEEE Statistical Signal Processing Workshop 2016 - Palma de Mallorca, Spain
Duration: 25 Jun 201629 Jun 2016


Conference19th IEEE Statistical Signal Processing Workshop 2016
Abbreviated titleSSP 2016
CityPalma de Mallorca


  • Bayesian Estimation
  • Hamiltonian Monte Carlo
  • Multifractal Analysis
  • Multivariate image
  • Texture Analysis

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications


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