Magnetic Tomography by Random Spatial Sampling

The Magnetic Tomography (MT) is an imaging technique that aims at reconstructing an unknown electric current distribution flowing within a volume conductor from the measurements of its magnetic field in the outer space. Among the other imaging techniques, MT has the advantage to be noninvasive and to have a high temporal resolution. For these reasons MT has applications in several fields, from geophysics to archeology, from nondestructive analysis of structures to medical tomography. MT devices do not give immediately an image of the electric current that flows in the conductor under study. Actually, to reconstruct the unknown current distribution from the magnetic data an highly ill-posed and ill-conditioned inverse problem has to be solved. We propose to solve the MT inverse problem by an inversion method based on the random sampling of the source space. The main advantage of the method is the dimensionality reduction that makes the method fast and the storage requirements very low. Moreover, the method can be easily applied to conductors of any shape. Some numerical tests showing the performances of the method on both synthetic and real data will be shown.