Abel inversion using total variation regularization: applications

We apply total-variation (TV) regularization methods to Abel inversion tomography. Inversions are performed using the fixed-point iteration method and the regularization parameter is chosen such that the resulting data fidelity approximates the known or estimated statistical character of the noisy data. Five one-dimensional (1D) examples illustrate the favorable characteristics of TV-regularized solutions: noise suppression and density discontinuity preservation. Experimental and simulated examples from X-ray radiography also illustrate limitations due to a linear projection approximation. TV-regularized inversions are shown to be superior to squared gradient (Tikhonov) regularized inversions for objects with density discontinuities. We also introduce an adaptive TV method that utilizes a modified discrete gradient operator acting only apart from data-determined density discontinuities. This method provides improved density level preservation relative to the basic TV method.