Click here to flash read.
Many real-life signals are defined on spherical domains, in particular in
geophysics and physics applications. In this work, we tackle the problem of
extending the iterative filtering algorithm, developed for the decomposition of
non-stationary signals defined in Euclidean spaces, to spherical domains. We
review the properties of the classical Iterative Filtering method, present its
extension, and study its convergence in the discrete setting. In particular, by
leveraging the Generalized Locally Toeplitz sequence theory, we are able to
characterize spectrally the operators associated with the spherical extension
of Iterative Filtering, and we show a counterexample of its convergence.
Finally, we propose a convergent version, called Spherical Iterative Filtering,
and present numerical results of its application to spherical data.
No creative common's license