Magnetic Doppler Imaging: Mathematical Basis

Dept. of Astronomy & Space Physics, Uppsala University, 751 20 Uppsala, Sweden

Abstract

We address important mathematical properties of solutions of the Magnetic Doppler Imaging problem. We show that the underlying inverse problem based on all 4 Stokes parameters is well-posed and thus has a unique solution. The only purpose of regularization is to suppress instabilities induced by sparse sampling of phase and/or wavelength when dealing with practical data. Therefore, the final solution is stable with respect to the initial guess and is not affected by the selection of a specific type of regularization.