Iterative alternating sequential (IAS) method for radio tomography of asteroids in 3D

We present a feasibility study of the radio tomography of asteroids. We consider the simplest and most robust type of a radio experiment and physical model, related to the CONSERT (Comet Nucleus Sounding Experiment by Radiowave Transmission) setup, where an orbiter measures the propagation time and amplitude of a radio frequency signal between the orbiter and a transponder placed on an asteroidʹs surface. Contrary to CONSERT, we consider the simultaneous use of multiple transponders. We study two main questions: (i) what is the basic information content (reconstruction potential) of the data and the minimum number of transponders for recovering most of it and (ii) how to formulate Bayesian methods for an efficient 3D reconstruction. Our approach was to reconstruct the perturbations of a non-constant refractive index inside the asteroid based on simulated signal travel time measurements. We formulate this ill-posed inverse problem by an approximative linear forward (data prediction) model through optical path length and Snellʹs law, resulting in a formula closely related to the cone-beam and Radon transforms. The linear forward model was applied to three-dimensional asteroid geometries involving an isotropic and piecewise constant refractive index distribution composed of the unknown perturbation and a background given a priori. The inverse approach was based on a hierarchical Bayesian model. The reconstructions were produced via the iterative alternating sequential (IAS) maximum a posteriori (MAP) estimation algorithm. We explored the various aspects of the problem by considering the recovery of empty cavities inside an asteroid. Two different transponder setups, a spherical and a realistic computation geometry, as well as various cavity distributions were tested. The results suggest that (i) the information content of the travel time data is robust and allows a unique reconstruction with suitable methods; (ii) finding a reasonable reconstruction requires the use of more than three transponders; (iii) reconstructions with the hierarchical prior model can be superior to those corresponding to Tikhonov regularized solution of the inverse problem; and (iv) producing an appropriate reconstruction necessitates finding a balance regarding the maximal number of reflections taken into account in the forward simulation, in order not to end up with a too sparse or noisy set of data.