Improved thermospheric neutral density models are required for the reduction of orbit prediction errors for satellites experiencing atmospheric drag. This research describes a new method to estimate density using a tomography-based approach, inspired by X-ray computed tomography from the medical imaging field. The change in specific mechanical energy of the orbit is used as the measurement, which is related to the integrated drag acceleration over the orbit. Using several such measurements from a number of satellites, one can estimate a spatially resolved multiplicative correction to an assumed density model. The problem considered here uses simulated measurements from 50 low-Earth orbit satellites and solves for the correction factor discretized over 324 grid elements spanning 300 to 500 km altitude. This ill-posed problem is solved using Tikhonov regularization, with the three-dimensional gradient as the regularization operator, resulting in a penalty on the spatial smoothness of the estimated density. Simulation results show that the true time-averaged density can be reconstructed to within approximately 10%, using only assumed ground-based tracking measurements separated over 12 hours.