Inversion of space-borne remote sensing measurements of the resonantly scattered solar Lyman alpha (121.6-nm) emission in planetary atmospheres is the most promising means of quantifying the H density in a vast volume of space near terrestrial planets. Owing to the highly nonlinear nature of the inverse problem and the lack of sufficient data constraints over the large volume of space where H atoms are present, previous inversion methods relied on physics-based parametric formulations of the H density distributions to guarantee solution uniqueness. Those physical formulations, such as the Chamberlain model, were developed with simple assumptions of the atmospheric conditions. The use of such formulations as constraints significantly limits the range of possible solutions, which might lead to large errors in the case when those assumptions are invalid. In this study, we demonstrate for the first time the feasibility of estimating the H density through regularized nonlinear inversion of the Ly-*α* emission in an optically thick atmosphere, without using parametric formulations. Specifically, Occam{\textquoteright}s inversion algorithm is used to demonstrate that the H density can be estimated in a large volume of space near the planet, with accuracy in different atmospheric regions depending on the observation scheme. Two distinctly different schemes are examined, including a low-Earth orbit and a geostationary orbit. Modeling results show that the low-Earth orbit is better for H density estimation in the thermosphere, while the high-altitude orbit is better for estimation in the exosphere. Our results could provide useful information for designing the observation schemes of future missions.