Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm

E. Loli Piccolomini (), V. L. Coli (), E. Morotti () and L. Zanni ()
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E. Loli Piccolomini: University of Bologna
V. L. Coli: University of Modena and Reggio Emilia
E. Morotti: University of Padova
L. Zanni: University of Modena and Reggio Emilia

Computational Optimization and Applications, 2018, vol. 71, issue 1, No 8, 191 pages

Abstract: Abstract 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.

Keywords: 3D Computed tomography; Image reconstruction; Total variation regularization; Nonnegatively constrained minimization; Scaled gradient projection methods (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10589-017-9961-2

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