Reconstructing surface permittivity distributions from RADAR measurements using a sparsity inducing regularized least-squares approach

The estimation of surface properties of small bodies in our solar system like asteroids, comets and small moons from RADAR observations is a particularly challenging task. Due to limitations in orbitography and instrument dynamics the associated inverse problems are usually ill-posed. Common methods in the solution of these kind of problems are regularized least-squares approaches where the proper selection of the parameter weighting target function and regularization penalty is of great importance and not trivial. In this paper we propose a methodology based on a compressive sensing technique and demonstrate its feasibility on a surface permittivity reconstruction based on the well known method of physical optics (PO). We show that the proposed algorithm yields proper and stable reconstruction results in a sparse representation of the surface permittivity distribution for sub-optimal choices of the regularization parameter.