In a previous study we performed a statistical analysis of the geosynchronous plasma environment from measurements of the magnetospheric plasma analyzer instruments aboard the Los Alamos geosynchronous spacecraft. In that study the mean spin-averaged particle fluxes were determined as a function of local time and Kp index, averaged over an entire year of observations. Particles on open drift trajectories should cross geosynchronous orbit twice during their drift from the nightside plasma sheet, through the inner magnetosphere, and out to the dayside magnetopause. The ratio of incoming plasma sheet phase space density and outgoing dayside phase space density of every drift path thus contains information about particle losses during the drift through the near-Earth region. For ions the losses are largely caused by charge exchange reactions with hydrogen atoms. Applying tomographic inversion techniques, we use the observed statistical losses inside the geosynchronous orbit region to infer the spatial distribution of exospheric neutral hydrogen. The particle drift paths from the nightside of geosynchronous orbit to the dayside are calculated from electric and magnetic field models. To test the sensitivity of the tomography to the convection model, we invert the geosynchronous particle observations using various field model combinations and compare the results. We find that the neutral hydrogen densities obtained from the inversion disagree with existing models of the exosphere, mainly in the near-Earth region. These differences are due to lower-than-expected losses of lower-energy particles that nominally drift through the inner region and/or particle sources not considered in the study.