Alexandra Koulouri and Maria Petrou
Vector Tomography, Ill Posedness, Regularisation, Inverse Problem
We revisit the problem of the reconstruction of an irrotational vector field by solving a set of line integral equations in the discrete domain. We show that the continuous inverse Radon formulation fails to reconstruct an irrotational vector field while the approximate solution of the problem in the digital domain is feasible, overcoming the intrinsic ill-posedness of the problem. In particular, we prove that the discretization of the problem is an efficient way of regularising the continuous ill posedness since it ensures an upper bound to the solution error. We demonstrate the effectiveness of the method with simulations.
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