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Abstract:
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We propose a wavelet-based spectral method for estimating the Hurst parameter in isotropic and anisotropic nonstationary fractional Gaussian fields. The method can be applied to self-similar images and, in general, to $d$-dimensional data that scale. In the application part, we consider denoising of 2-D fractional Brownian fields and the classification of the clouds/temperature satellite images. In the first application, we use Bayesian inference in the wavelet-spectral domain to separate the signal (the Brownian field) and noise. For the classification of geophysical images we first estimate directional Hurst exponents and use them as an input to standard machine learning algorithms. This work is joint with Orietta Nicolis, University of Bergamo, and Claudio Garutti, University of Padova, Italy.
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