Affiliations: [a] National Digital Switching System Engineering and Technological R&D Centre , Zhengzhou, Henan, China | [b] Department of Nephrology, the First Affiliated Hospital of Zhengzhou University, Zhengzhou, Henan, China
Correspondence:
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Corresponding author: Bin Yan, National Digital Switching System Engineering and Technological R & D Centre, Zhengzhou, Henan 450002, China. E-mail:ybspace@hotmail.com
Abstract: Iterative reconstruction algorithms for computed
tomography (CT) through total variation regularization based on piecewise
constant assumption can produce accurate, robust, and stable results.
Nonetheless, this approach is often subject to staircase artefacts and the
loss of fine details.
To overcome these shortcomings, we introduce a family of
novel image regularization penalties called total generalized variation
(TGV) for the effective production of high-quality images from incomplete or
noisy projection data for 3D reconstruction.
We propose a new, fast alternating direction minimization
algorithm to solve CT image reconstruction problems through TGV
regularization. Based on the theory of sparse-view image reconstruction and
the framework of augmented Lagrange function method, the TGV regularization
term has been introduced in the computed tomography and is transformed into
three independent variables of the optimization problem by introducing
auxiliary variables. This new algorithm applies a local linearization and
proximity technique to make the FFT-based calculation of the analytical
solutions in the frequency domain feasible, thereby significantly reducing
the complexity of the algorithm.
Experiments with various 3D datasets corresponding to
incomplete projection data demonstrate the advantage of our proposed
algorithm in terms of preserving fine details and overcoming the staircase
effect. The computation cost also suggests that the proposed algorithm is
applicable to and is effective for CBCT imaging.
Theoretical and technical optimization should be
investigated carefully in terms of both computation efficiency and high
resolution of this algorithm in application-oriented research.
Keywords: Computed tomography, iterative reconstruction, total generalized variation, alternating direction method
