Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm
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 re...
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Veröffentlicht in: | Computational optimization and applications 2018-09, Vol.71 (1), p.171-191 |
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creator | Piccolomini, E. Loli Coli, V. L. Morotti, E. Zanni, L. |
description | 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. |
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Loli ; Coli, V. L. ; Morotti, E. ; Zanni, L.</creator><creatorcontrib>Piccolomini, E. Loli ; Coli, V. L. ; Morotti, E. ; Zanni, L.</creatorcontrib><description>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.</description><identifier>ISSN: 0926-6003</identifier><identifier>EISSN: 1573-2894</identifier><identifier>DOI: 10.1007/s10589-017-9961-2</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Computed tomography ; Convex and Discrete Geometry ; Ill posed problems ; Image reconstruction ; Management Science ; Mathematics ; Mathematics and Statistics ; Nonlinear programming ; Operations Research ; Operations Research/Decision Theory ; Optimization ; Projection ; Regularization ; Scaling ; Statistics</subject><ispartof>Computational optimization and applications, 2018-09, Vol.71 (1), p.171-191</ispartof><rights>Springer Science+Business Media, LLC 2017</rights><rights>Computational Optimization and Applications is a copyright of Springer, (2017). 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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. 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subjects | Algorithms Computed tomography Convex and Discrete Geometry Ill posed problems Image reconstruction Management Science Mathematics Mathematics and Statistics Nonlinear programming Operations Research Operations Research/Decision Theory Optimization Projection Regularization Scaling Statistics |
title | Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm |
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