The tomography of the Earth's atmosphere by the solar occultation method leads to a highly non-linear inverse problem if the full solar disc is used as the light source. Well known heuristic methods like Chahine's algorithm or onion peeling fail to solve the inversion. We present a new method referred to as NOPE (for natural orthogonal polynomial expansion) that addresses this class of inverse problems by focusing on the morphological content of the unknown profile and allowing also a fine tuning of the a priori information.