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In this work we report the successful application of an innovative method, based on the Sparse Representation of signals, to perform a real-time, unsupervised detection of the individual components in a frequency degenerate, multi-harmonic spectrum, using a small number of data un-evenly sampled in the spatial domain. This method has been developed from its original applications in astronomy, and is now routinely used in the JET thermonuclear fusion experiment to obtain the decomposition of a spectrum of high-frequency (~10-500kHz range) magnetic instabilities with a sub-ms time resolution, allowing the real-time tracking of its individual components as the plasma background evolves. This work opens a path towards developing real-time control tools for electro-magnetic instabilities in future fusion devices aimed at achieving a net energy gain. More generally, the speed and accuracy of this algorithm is recommended for instances of physics measurements and control engineering where an unsupervised, real-time decomposition of a degenerate signal is required from a small number of data.