This paper outlines a new mathematical approach to imaging the electron density distribution in the high regions of the topside ionosphere and the plasmasphere from 800 km up to 20,200 km altitude using GPS measurements from low Earth orbit (LEO) satellites. The problem of ionospheric imaging using ground-based GPS measurements has been studied for a number of years. Such methods have proved extremely useful in providing details of the larger-scale morphology of the global ionosphere. The work presented extends these methods to image the plasmasphere up to altitudes of the GPS satellites at 20,000 km. The problem of limited observations due to the small number of LEOs in operation is overcome by constraining the plasmaspheric electron density to be constant along magnetic field lines. A coordinate transform from a spherical coordinate system to one defined in terms of Euler potentials is sufficient to provide unambiguous solutions. Preliminary results using data from the COSMIC satellite constellation are presented showing the response of the plasmasphere to changes in the interplanetary medium.