Speaker
Description
In signal processing, the time-frequency analysis of nonlinear and non-stationary processes, as well as the determination of the unknown number of active sub-signals in a blind-source composite signal, are generally challenging inverse problem tasks. If we consider data sampled on a sphere, things get even more complicated. This is the reason why just a few techniques have been developed so far to study this kind of data. However, many real-life data are of this nature, like in Geophysics and Physics.
The idea is to extend the Iterative Filtering (IF) algorithm to work on the sphere. IF is a non-stationary signal decomposition method proposed a decade ago [Lin et al. 2009] to address the problem of extracting time-varying oscillatory components from a non-stationary multicomponent signal. This method proved to be really valuable in many applications, see [Barbarino&Cicone 2022] and references therein, and it was accelerated in what is known as Fast Iterative Filtering (FIF) [Cicone&Zhou 2021] by leveraging the Toeplitz matrix theory. In this talk, we introduce the generalization of IF to handle spherical data and show how we can address the question about its convergence [Barbarino et al 2024]. We conclude with some examples of application to geophysical data.
L. Lin, Y. Wang, and H. Zhou. Iterative filtering as an alternative algorithm for empirical mode decomposition. Adv. in Adap. Data An., 2009, 1.04, 543-560.
G. Barbarino, A. Cicone. Conjectures on spectral properties of ALIF algorithm. Linear Algebra and its Applications, Volume 647, Pages 127-152, 2022.
A. Cicone, H. Zhou. Numerical Analysis for Iterative Filtering with New Efficient Implementations Based on FFT. Num. Math., 2021, 147 (1), 1–28.
G. Barbarino, R. Cavassi, A. Cicone. Extension and convergence analysis of Iterative Filtering to spherical data. Linear Algebra and its Applications, 2024.
