Knowledge of the three-dimensional spatial structure of Earth's uppermost atmosphere is necessary both to understand its role as a dynamic buffer against the solar-driven environment of interplanetary space as well as to assess the rate of its permanent escape from Earth's gravity through evaporation. The only available means of inferring atmospheric structure at these altitudes is through space-based remote sensing of solar radiation that is resonantly scattered or fluoresced by the ambient atoms. In this paper, the resultant tomographic image formation problem is formulated as an edge-preserving reconstruction algorithm based on the framework originally proposed by Mumford & Shah. Statistical interpretation of this reconstruction solution is formulated in the context of MAP estimation. The numerical results illustrate that the proposed reconstruction algorithm is capable of obtaining physically meaningful solutions that are superior to previous results formulated based on parametric assumptions on the unknown density.