Efficient, real-time and unsupervised data analysis is one of the key elements for achieving scientific success in complex engineering and physical systems, of which three examples are the currently operating Joint European Torus (JET) and the soon-to-be-built International Thermonuclear Experimental Reactor (ITER) and the Square Kilometre Array (SKA) telescope. There is a wealth of signal processing techniques that are being applied to data analysis in such complex systems, and here we wish to present some examples of the synergies that can be exploited when combining ideas and methods from different fields, such as astronomy and astrophysics and thermonuclear fusion plasmas. One problem which is common to these subjects is the determination of pulsation modes from irregularly sampled time-series. We have used recent techniques of signal processing in astronomy and astrophysics, based on the Sparse Representations of Signals, to solve current questions arising in thermonuclear fusion plasmas. Two examples 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. 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 and of the SKA telescope will be discussed. Finally, we will conclude with an example of a potential application of the Sparse Representation method to the analysis of electrical prospections (using the so-called Schlumberger diagram) in an Etruscan necropolis and in an Etruscan fortress town located close to Rome, both sites dating from around the fifth century BC.