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Brani Vidakovic, Georgia Tech

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All That Scaling
17 March 2016 from 4:00 PM to 5:00 PM
201 Thomas Building
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Brani VidakovicIn this talk we overview the wavelet-based estimation of scaling
indices of self-similar time series and images. We consider a range of wavelet and wavelet-like decompositions: orthogonal,
non-decimated, wavelet packets, complex-valued decompositions, autocorrelation shells of wavelets, and spherical wavelets. They
all result in a hierarchy of imbedded multiresolution subspaces that produce a valid multiscale spectra. Like in the Fourier
transforms where the linear decay in log-power spectra over the frequencies characterizes the regularity/smoothness of a time
series/image, the decay of the log-averaged squared wavelet coefficients leads to an alternative and arguably more local and
stable measure of signal regularity. We also provide examples from medicine, finance, and geosciences in which the scaling indices
turn out to be useful in tasks of statistical learning.

In the talk we also briefly overview some traditional results, some results from the research, research of the speaker and his
collaborators, as well as some interesting results from the ongoing research. We will point out at several avenues for possible future research.

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