We propose a scaled gradient projection algorithm for the reconstruction of 3D X-ray tomographic images from limited data. The problem arises from the discretization of an ill-posed integral problem and, due to the incompleteness of the data, has infinite possible solutions. Hence, by following a regularization approach, we formulate the reconstruction problem as the nonnegatively constrained minimization of an objective function given by the sum of a fit-to-data term and a smoothed differentiable Total Variation function. The problem is challenging for its very large size and because a good reconstruction is required in a very short time. For these reasons, we propose to use a gradient projection method, accelerated by exploiting a scaling strategy for defining gradient-based descent directions and generalized Barzilai-Borwein rules for the choice of the step-lengths. The numerical results on a 3D phantom are very promising since they show the ability of the scaling strategy to accelerate the convergence in the first iterations.

Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm / Piccolomini, E. Loli; Coli, V. L.; Morotti, E.; Zanni, L.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - 71(2018), pp. 171-191.

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