统计内体积成像
Statistical interior tomography.
机构信息
Institute of Image Processing and Pattern Recognition, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China.
出版信息
IEEE Trans Med Imaging. 2011 May;30(5):1116-28. doi: 10.1109/TMI.2011.2106161. Epub 2011 Jan 13.
Abstract
This paper presents a statistical interior tomography (SIT) approach making use of compressed sensing (CS) theory. With the projection data modeled by the Poisson distribution, an objective function with a total variation (TV) regularization term is formulated in the maximization of a posteriori (MAP) framework to solve the interior problem. An alternating minimization method is used to optimize the objective function with an initial image from the direct inversion of the truncated Hilbert transform. The proposed SIT approach is extensively evaluated with both numerical and real datasets. The results demonstrate that SIT is robust with respect to data noise and down-sampling, and has better resolution and less bias than its deterministic counterpart in the case of low count data.
摘要
本文提出了一种利用压缩感知（CS）理论的统计内放射断层成像（SIT）方法。该方法通过泊松分布对投影数据进行建模，在最大后验（MAP）框架下，用一个具有全变差（TV）正则化项的目标函数来求解内部问题。该方法使用交替最小化方法来优化目标函数，初始图像来自截断 Hilbert 变换的直接反演。利用数值和真实数据集对所提出的 SIT 方法进行了广泛评估。结果表明，SIT 对数据噪声和降采样具有鲁棒性，并且在低计数数据的情况下，其分辨率比确定性方法更好，偏差更小。
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