Spectral line profiles from light, atomic gases in upper planetary atmospheres are commonly non-Maxwellian. The velocity distributions of these light gases are perturbed in complex ways by atmospheric escape processes, by the paucity of thermalizing collisions, and by infrequent but important collisions with hot ions in the plasmasphere. It has long been recognized that the velocity distributions can be used to unfold the physical processes leading to atmospheric escape and to the partitioning of neutral gas trajectory classifications (ballistic, escaping, or satellite). Unfortunately, isolation of the velocity distribution from the measured emission line profile is not a simple matter, especially when neither of the velocity distributions are non- Maxwellian and when the instrument function used to measure the profile is also a complex function. We have experimented with several techniques to accurately retrieve the velocity distribution of atomic hydrogen in the earth's exosphere from the hydrogen Balmer-alpha (H(alpha )) emission line profile measured with a Fabry-Perot interferometer. Although the derived velocity distribution remains subject to contamination of the measured emission by extraterrestrial and terrestrial sources, the technique to decompose the actual emission function from the combined instrument function plus emission function is established in this work -- and is applicable to many other similar problems. In particular, two techniques are compared. First, a classical deconvolution technique is developed using objective, low-pass filtering. Second, a nonlinear deconvolution algorithm, commonly referred to as `CLEAN' by the radio astronomy community that developed it, is applied to the optical H(alpha ) spectra. We find that this second technique is useful for an accurate isolation of the velocity distribution of atomic hydrogen in earth's exosphere, while the classical deconvolution is more useful for determining the full width at half maximum of the emission. The CLEAN technique does a superior job of isolating low signal-to-noise information in the emission profile wings, of particular interest for the derivation of the escaping atomic hydrogen population. It is particularly important that the CLEAN technique, when properly applied, is not susceptible to the addition of unrealistic information in the low signal-to-noise region of emission line extrema, whereas common deconvolution techniques are often quite suspect in these regions. Using this new technique and a new ability to ascribe hydrogen column abundance to H(alpha ) brightness measurements, we are now poised to derive atomic hydrogen escape fluxes without dependence upon models of escape flux dynamics.