Tomography of the solar corona. I. A robust, regularized, positive estimation method

A general method for the reconstruction of emissivity structures in the sol ar corona from projection data is presented. The method creates a robust, r egularized, positive estimate (RRPE) of the coronal emissivity distribution . The problem of reconstructing the three-dimensional emissivity from a tim e series of coronagraph images is considered in detail. The discussion is s et in the framework of the robust solution of underdetermined, linear syste ms of equations. In two-dimensional numerical experiments, the RRPE method is compared to the multiplicative algebraic reconstruction technique (MART) , and the superiority of RRPE is demonstrated. The most important and restr ictive assumptions upon which the methodology is based are (1) that the str ucture of the corona does not vary with time and (2) that there are enough coronagraph images to resolve the longitudinal structures of the corona. Th e consequences of these assumptions are not addressed here but will be stud ied in future work. The three-dimensional reconstruction of the coronal ele ctron density from a time series of actual coronagraph images is deferred t o a subsequent paper in this series.