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首页> 外文期刊>IEEE Transactions on Nuclear Science >Few-view computed tomography image reconstruction using mean curvature model with curvature smoothing and surface fitting
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Few-view computed tomography image reconstruction using mean curvature model with curvature smoothing and surface fitting

机译：使用具有曲率平滑和表面拟合的平均曲率模型重建少数视图计算机断层摄影图像

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摘要

The edge and curve of an image surface are crucial visual cues in vision psychology. Studies show that human beings can effectively process curvature information, such as distinguishing the concavity and convexity of an image. This finding indicates that curvature is essential for a desired image to be felt authentic and real. In this paper, a novel few-view computed tomography (CT) image reconstruction model is proposed based on mean curvature (MC). Similar to the total variation model, the MC employs the L-1-norm to utilize the sparse prior information. Constructing efficient numerical algorithms for minimizing the MC model is significant due to the associated high-order Euler-Lagrange equations. A two-step numerical method, including curvature smoothing and surface fitting, is presented to solve the proposed model, which can be stably and efficiently solved by the alternating direction minimization. By applying the variable splitting method, the explicit solutions of the corresponding subproblems can be efficiently and quickly approximated by fast Fourier transform and the proximal point method. The accuracy and efficiency of the simulated and real data are qualitatively and quantitatively evaluated to verify the efficiency and feasibility of the proposed method. Comparisons with conventional algorithms demonstrate that the proposed approach has considerable advantages in few-view CT reconstruction problems.
机译：图像表面的边缘和曲线是视觉心理学中至关重要的视觉提示。研究表明，人类可以有效地处理曲率信息，例如区分图像的凹凸。这一发现表明，曲率对于使想要的图像真实可信是至关重要的。本文提出了一种基于平均曲率（MC）的新型少视计算机断层扫描（CT）图像重建模型。类似于总变异模型，MC使用L-1-范数来利用稀疏先验信息。由于相关的高阶Euler-Lagrange方程，构造有效的数值算法以最小化MC模型非常重要。提出了一种包括曲率平滑和曲面拟合的两步数值方法来求解该模型，该方法可以通过交替方向最小化而稳定有效地求解。通过应用变量分裂方法，可以通过快速傅里叶变换和近点方法有效，快速地逼近相应子问题的显式解。定性和定量地评估了模拟数据和真实数据的准确性和效率，以验证该方法的有效性和可行性。与常规算法的比较表明，所提出的方法在少数视图CT重建问题中具有相当大的优势。

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