Tomography of the Solar Corona. I. A Robust, Regularized, Positive Estimation Method

A general method for the reconstruction of emissivity structures in the solar corona from projection data is presented. The method creates a robust, regularized, positive estimate (RRPE) of the coronal emissivity distribution. The problem of reconstructing the three-dimensional emissivity from a time series of coronagraph images is considered in detail. The discussion is set in the framework of the robust solution of underdetermined, linear systems 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 restrictive assumptions upon which the methodology is based are (1) that the structure of the corona does not vary with time and (2) that there are enough coronagraph images to resolve the longitudinal structures of the corona. The consequences of these assumptions are not addressed here but will be studied in future work. The three-dimensional reconstruction of the coronal electron density from a time series of actual coronagraph images is deferred to a subsequent paper in this series.