Pattern recognition techniques in Polarimetry

Sparsity is a property of data by which it can be represented using a small number of patterns. It is the key concept behind an evergrowing list of mathematical techniques for handling data and recover from it signals or information in conditions previously thought impossible. The application of those techniques to spectropolarimetric data is relatively straightforward. We present three examples of such application: the use of Principal Component Analysis to invert the magnetic field in solar prominences from spectropolarimetry of the He D₃ line, the removal of fringes from spectropolarimetric data with Relevance Vector Machines, and the retrieval of high resolution spectra from low resolution data with Compressed Sensing.