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二维CT的二次正则化设计

Quadratic regularization design for 2-D CT.

作者信息

Shi Hugo R, Fessler Jeffrey A

机构信息

Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109 USA.

出版信息

IEEE Trans Med Imaging. 2009 May;28(5):645-56. doi: 10.1109/TMI.2008.2007366. Epub 2008 Oct 31.

DOI:10.1109/TMI.2008.2007366
PMID:19272993
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC2911484/
Abstract

Statistical methods for tomographic image reconstruction have improved noise and spatial resolution properties that may improve image quality in X-ray computed tomography (CT). Penalized weighted least squares (PWLS) methods using conventional quadratic regularization lead to nonuniform and anisotropic spatial resolution due to interactions between the weighting, which is necessary for good noise properties, and the regularizer. Previously, we addressed this problem for parallel-beam emission tomography using matrix algebra methods to design data-dependent, shift-variant regularizers that improve resolution uniformity. This paper develops a fast angular integral mostly analytical (AIMA) regularization design method for 2-D fan-beam X-ray CT imaging, for which parallel-beam tomography is a special case. Simulation results demonstrate that the new method for regularization design requires very modest computation and leads to nearly uniform and isotropic spatial resolution in transmission tomography when using quadratic regularization.

摘要

断层图像重建的统计方法改善了噪声和空间分辨率特性，这可能会提高X射线计算机断层扫描（CT）的图像质量。使用传统二次正则化的惩罚加权最小二乘法（PWLS）由于加权（这对于良好的噪声特性是必要的）与正则化器之间的相互作用，导致空间分辨率不均匀且各向异性。此前，我们针对平行束发射断层扫描解决了这个问题，使用矩阵代数方法设计依赖于数据的、移位变体正则化器，以提高分辨率均匀性。本文为二维扇形束X射线CT成像开发了一种快速角积分大多解析（AIMA）正则化设计方法，平行束断层扫描是其特殊情况。模拟结果表明，新的正则化设计方法计算量非常小，并且在使用二次正则化时，在透射断层扫描中可实现近乎均匀且各向同性的空间分辨率。

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