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首页> 外文期刊>Applied Mathematical Modelling >A variational proximal alternating linearized minimization in a given metric for limited-angle CT image reconstruction
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A variational proximal alternating linearized minimization in a given metric for limited-angle CT image reconstruction

机译：给定度量中的变分近端交替线性化最小化用于有限角度CT图像重建

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摘要

Due to the restriction of computed tomography (CT) scanning environment, the acquired projection data may be incomplete for exact CT reconstruction. Though some convex optimization methods, such as total variation minimization based method, can be used for incomplete data reconstruction, the edge of reconstruction image may be partly distorted for limited-angle CT reconstruction. To promote the quality of reconstruction image for limited-angle CT imaging, in this paper, a nonconvex and nonsmooth optimization model was investigated. To solve the model, a variational proximal alternating linearized minimization (VPALM) method based on proximal mapping in a given metric was proposed. The proposed method can avoid computing the inverse of a huge system matrix thus can be used to deal with the larger-scale inverse problems. What's more, we show that each bounded sequence generated by VPALM globally converges to a critical point based on the Kurdyka-Lojasiewicz property. Real data experiments are used to demonstrate the viability and effectiveness of VPALM method, and the results show that the proposed method outperforms two classical CT reconstruction methods. (C) 2018 Elsevier Inc. All rights reserved.
机译：由于计算机断层扫描（CT）扫描环境的限制，对于精确的CT重建，获取的投影数据可能不完整。尽管某些凸优化方法（例如基于总变化量最小化的方法）可用于不完整的数据重建，但对于有限角度CT重建，重建图像的边缘可能会部分变形。为了提高有限角度CT成像重建图像的质量，本文研究了一种非凸且非平滑的优化模型。为了解决该模型，提出了基于给定度量中基于近端映射的变分近端交替线性最小化（VPALM）方法。所提出的方法可以避免计算庞大的系统矩阵的逆，因此可以用于处理较大规模的逆问题。此外，我们显示了VPALM生成的每个有界序列都基于Kurdyka-Lojasiewicz属性全局收敛到一个临界点。实际数据实验证明了VPALM方法的可行性和有效性，结果表明该方法优于两种经典的CT重建方法。 （C）2018 Elsevier Inc.保留所有权利。

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