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

By Elena LOLI PICCOLOMINI, Vanna Lisa Coli, E Morotti and Luca Zanni


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 Barzilaiâ\u80\u93Borwein 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

Topics: 3D Computed tomography, Image reconstruction, Nonnegatively constrained minimization, Scaled gradient projection methods, Total variation regularization, Control and Optimization, Computational Mathematics, Applied Mathematics
Year: 2017
DOI identifier: 10.1007/s10589-017-9961-2
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