Bayesian multifractal analysis of multi-temporal images using smooth priors

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.