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 and blind detection of the individual components in a frequency degenerate, multi-harmonics 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 Joint European Torus thermonuclear fusion experiment to obtain the decomposition of a spectrum of high-frequency (~10-500kHz range) magnetic instabilities with a faster-than-1ms time resolution, allowing the real-time tracking of its individual components as the plasma background evolves. This work opens a clear path towards developing real-time control tools for electro-magnetic instabilities in future fusion devices aimed at achieving a net energy gain, such as the ITER facility currently being built in France. More generally, the very high speed and accuracy of this algorithm is recommended for application to instances of physics measurements and control engineering where a real-time, blind and unsupervised decomposition of a degenerate input signal is required from a small number of data.