Title
Wavelet based processing of geophysics signals: Anova-like decompositions and (multi)fractality assessment
Speaker
Brani Vidakovic, Department of Industrial & Systems Engineering, Georgia Institute of Technology
Abstract
Denoising and density estimation are paradigmatic statistical applications of wavelets with a large body of research in the last 10 years. The focus of statistical community shifts now to utilizing wavelets in the context of more general statistical models. An example are generalized linear models.
In this talk we apply wavelets in the context of functional Anova, in which a treatment-effect separation and the smoothing process are combined in a single procedure. Our separation/shrinkage process is model based, in particular we discuss the Bayesian modeling in the wavelet domain and shrink utilizing the optimal rules with respect to the proposed model.
We apply the method on 1- and 2-D signals from geophysics (turbulence and cloud IR imagery). One of the benefits of applying Bayesian shrinkage on natural signals is the existence of universal power laws by which our priors can be calibrated.
