Sparse representation of signals: from astrophysics to real-time data analysis for fusion plasmas and system optimization analysis for ITER and TCV

Efficient, real-time and automated data analysis is one of the key elements for achieving scientific success in complex engineering and physical systems, of which two examples are the JET and ITER tokamaks. One problem which is common to these fields is the determination of pulsation modes from irregularly sampled time-series. To this end, there is a wealth of signal processing techniques that are being applied to post-pulse and real-time data analysis in such complex systems. Here we wish to present a review of the applications of a method based on the Sparse Representation of Signals, using examples of the synergies that can be exploited when combining ideas and methods from very different fields, such as astronomy and astrophysics and thermonuclear fusion plasmas. Examples of this work in astronomy and astrophysics are the analysis of pulsation modes in various classes of stars and the orbit determination software of the Pioneer spacecrafts. Two examples of this work in thermonuclear fusion plasmas are the detection of magneto-hydrodynamic instabilities, which is now performed routinely in JET in real-time on a sub-millisecond time-scale, and the studies leading to the optimization of the magnetic diagnostic system in ITER and TCV. These questions have been solved formulating them as inverse problems, despite the fact that these applicative frameworks are extremely different from the classical use of Sparse Representations, on both the theoretical and computational points of view. Requirements, prospects and ideas for the signal processing and real-time data analysis applications of this method to routine operation of ITER will also be discussed. Finally, a very recent development has been an attempt at the application of this method to the deconvolution of the measurement of electric potential performed during a ground-based survey of a proto-Villanovian necropolis in central Italy.