A Bayesian framework for the multifractal analysis of images using data augmentation and a whittle approximation

S. Combrexelle, H. Wendt, Yoann Altmann, J. Y. Tourneret, Stephen McLaughlin, P. Abry

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

Abstract

Texture analysis is an image processing task that can be conducted using the mathematical framework of multifractal analysis to study the regularity fluctuations of image intensity and the practical tools for their assessment, such as (wavelet) leaders. A recently introduced statistical model for leaders enables the Bayesian estimation of multifractal parameters. It significantly improves performance over standard (linear regression based) estimation. However, the computational cost induced by the associated nonstandard posterior distributions limits its application. The present work proposes an alternative Bayesian model for multifractal analysis that leads to more efficient algorithms. It relies on three original contributions: A novel generative model for the Fourier coefficients of log-leaders; an appropriate reparametrization for handling its inherent constraints; a data-augmented Bayesian model yielding standard conditional posterior distributions that can be sampled exactly. Numerical simulations using synthetic multifractal images demonstrate the excellent performance of the proposed algorithm, both in terms of estimation quality and computational cost.

Original languageEnglish
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
PublisherIEEE
Pages4224-4228
Number of pages5
ISBN (Print)9781479999880
DOIs
Publication statusPublished - 2016
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing 2016 - Shanghai International Convention Center, Shanghai, China
Duration: 20 Mar 201625 Mar 2016

Conference

Conference41st IEEE International Conference on Acoustics, Speech and Signal Processing 2016
Abbreviated titleICASSP 2016
CountryChina
CityShanghai
Period20/03/1625/03/16

Fingerprint

Linear regression
Costs
Image processing
Textures
Computer simulation
Statistical Models

Keywords

  • Bayesian Estimation
  • Data Augmentation
  • Multifractal Analysis
  • Wavelet Leaders
  • Whittle Likelihood

ASJC Scopus subject areas

  • Signal Processing
  • Software
  • Electrical and Electronic Engineering

Cite this

Combrexelle, S., Wendt, H., Altmann, Y., Tourneret, J. Y., McLaughlin, S., & Abry, P. (2016). A Bayesian framework for the multifractal analysis of images using data augmentation and a whittle approximation. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 4224-4228). IEEE. https://doi.org/10.1109/ICASSP.2016.7472473
Combrexelle, S. ; Wendt, H. ; Altmann, Yoann ; Tourneret, J. Y. ; McLaughlin, Stephen ; Abry, P. / A Bayesian framework for the multifractal analysis of images using data augmentation and a whittle approximation. 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. pp. 4224-4228
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Combrexelle, S, Wendt, H, Altmann, Y, Tourneret, JY, McLaughlin, S & Abry, P 2016, A Bayesian framework for the multifractal analysis of images using data augmentation and a whittle approximation. in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, pp. 4224-4228, 41st IEEE International Conference on Acoustics, Speech and Signal Processing 2016, Shanghai, China, 20/03/16. https://doi.org/10.1109/ICASSP.2016.7472473

A Bayesian framework for the multifractal analysis of images using data augmentation and a whittle approximation. / Combrexelle, S.; Wendt, H.; Altmann, Yoann; Tourneret, J. Y.; McLaughlin, Stephen; Abry, P.

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. p. 4224-4228.

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

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Combrexelle S, Wendt H, Altmann Y, Tourneret JY, McLaughlin S, Abry P. A Bayesian framework for the multifractal analysis of images using data augmentation and a whittle approximation. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE. 2016. p. 4224-4228 https://doi.org/10.1109/ICASSP.2016.7472473