Inverting ionospheric radio occultation measurements using maximum entropy

Practical aspects of the inversion of ionospheric radio occultation data using the Abel transform and its inverse are discussed. The linear inverse transform exhibits poor error propagation characteristics, producing significant artifacts preferentially at low altitudes where they might easily be mistaken for intermediate or sporadic layers in the ionosphere. Tikhonov regularization, which can be viewed as fixed linear filtering, reduces the artifacts at the expense of discarding fine structure in the profiles. Improved results are obtained using maximum entropy and Bayesian statistics. The maximum entropy algorithm can be viewed as a nonlinear adaptive filter which suppresses artifacts while preserving fine structure to the degree the data can support. Other advantages of and avenues for improving the basic maximum entropy algorithm are discussed.