Regularization Methods for the Solution of Inverse Problems in Solar X-ray and Imaging Spectroscopy

Astronomical practice often requires addressing remote sensing problems, whereby the radiation emitted by a source far in the sky and measured through ‘ad hoc’ observational techniques, contains very indirect information on the physical process at the basis of the emission. The main difficulties in this investigations rely on the poor quality of the measurements and on the ill-posedness of the mathematical model describing the relation between the measured data and the target functions. In the present paper we consider a set of problems in solar physics in the framework of the NASA Ramaty High Energy Solar Spectroscopic Imager (RHESSI) mission. The data analysis activity is essentially based on the regularization theory for ill-posed inverse problems and a review of the main regularization methods applied in this analysis is given. Furthermore, we describe the main results of these applications, in the case of both synthetic data and real observations recorded by RHESSI.