A tomographic forward and inverse model is presented that enables the recovery of three-dimensional ionospheric structures from space-based optical observations. In this paper we apply the technique to the Global Ultraviolet Imager (GUVI) on board the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite. The forward model is based on GUVI observation geometry to simulate radiance observations of a model ionosphere. This model incorporates the physics of the 1356 Å emission and the pattern of line-of-sight measurements out of the plane of the orbit into a discrete matrix representation of the GUVI observation. The application of matrix inversion techniques to the discrete observation matrix allows a multidimensional electron density profile to be reconstructed from the GUVI brightness measurements. Appropriate regularization functionals are incorporated to constrain the reconstructed solution. A smoothness constraint with a nonconvex penalty function ensures smoothness while preserving edges in the reconstructed image, an attribute which is crucial for the reconstruction of sharp ionospheric gradients. Results using GUVI data are shown to demonstrate the applicability of this technique.