Title: On statistical signal analysis via Fourier and optimal transport
Abstract: In this talk, we focus on the statistical analysis of signals by combining Fourier analysis with optimal transport. First, we demonstrate how optimal transport provides a relevant measure of (dis)similarity between time series by quantifying the displacement of their energy across frequencies in the Fourier domain. Based on this, we show how treating power spectral density as probability distributions endowed with optimal transport enables to implement a meaningful PCA to learn the main modes of variation of a dataset. Next, we discuss how the geometry induced by optimal transport allows for a natural geodesic interpolation between time series. Finally we illustrate this geometry with the generation of artificial audio signals that interpolates between given source and target sounds. The method we propose considers the spectrograms of the audio signals globally and does not operate on a temporal frame-to-frame basis.
Short bio : Elsa Cazelles is a CNRS researcher at the Research Institute of Informatics of Toulouse (IRIT). Her work focuses broadly on optimal transport for statistical data analysis. Elsa Cazelles holds a Ph.D in applied mathematics from the University of Bordeaux and has also worked as a postdoctoral fellow at the University of Chile.