Non-commutative Tomography: Applications to Data Analysis
Résumé
In this chapter, we briefly recall the theory of non-commutative tomography in a pedagogical way. We then consider its applications to signal analysis. The advantages and drawbacks of these techniques to finite samples of data are discussed. Then the method is applied, first to signals originating from reflectometry measurements in magnetized fusion plasmas, and then to data obtained from the advection of tracers in a two-dimensional time-dependent flow generated by three point vortices. In the first case, we show that the tomogram allows to pick a base to represent our signal which has the advantage of isolating the reflection coming from the plasma and then to improve the estimation of the density profile. In the second case, we show how, with a "tricky transformation" the method allows us to detect Lévy flights and extract some of their properties.