A filtered backprojection MAP algorithm with nonuniform sampling and noise modeling
A filtered backprojection MAP algorithm with nonuniform sampling and noise modeling
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DOI：
10.1118/1.3697736
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发表时间：
2012-04-01
期刊：
影响因子：
3.8
通讯作者：
Zeng, Gengsheng L.
中科院分区：
文献类型：
--
作者：
Zeng, Gengsheng L.
目的：本文的目标是扩展我们最近开发的FBP（滤波反投影）算法，它具有相同的特点的迭代Landweber算法，一个FBP算法具有相同的特点的迭代MAP（最大后验概率）算法。新开发的FBP算法也适用于角采样间隔不均匀的情况。投影噪声方差可以使用基于视图的加权方案来建模。方法：新的目标函数包含投影噪声模型相关加权因子和图像相关先验（即，贝叶斯术语）。噪声加权是基于逐个视图的。FBP算法首次能够对投影噪声进行建模。基于迭代Landweber MAP算法的公式化，对于Landweber MAP算法的每次迭代导出频域窗函数。结果，斜坡滤波器和窗口函数都被贝叶斯分量修改。结果：计算机模拟表明，新的窗口指数为k的FBP-MAP算法和迭代次数为k的Landweber MAP算法在分辨率和噪声纹理方面具有相似的重建效果。透射X射线CT的一个例子表明，噪声建模方法是能够显着减少条纹伪影与低剂量CT。结论：基于视图的噪声加权方案可以引入到FBP算法作为加权因子的窗口函数。新的FBP算法是能够提供类似的结果，迭代MAP算法，如果斜坡滤波器被修改与添加项。非均匀采样和灵敏度可以通过适当的反投影加权来调节。(C)2012年美国医学物理学家协会。[http：//dx.doi.org/10.1118/1.3697736]
Purpose: The goal of this paper is to extend our recently developed FBP (filtered backprojection) algorithm, which has the same characteristics of an iterative Landweber algorithm, to an FBP algorithm with the same characteristics of an iterative MAP (maximum a posteriori) algorithm. The newly developed FBP algorithm also works when the angular sampling interval is not uniform. The projection noise variance can be modeled using a view-based weighting scheme.Methods: The new objective function contains projection noise model dependent weighting factors and image dependent prior (i.e., a Bayesian term). The noise weighting is view-by-view based. For the first time, the FBP algorithm is able to model the projection noise. Based on the formulation of the iterative Landweber MAP algorithm, a frequency-domain window function is derived for each iteration of the Landweber MAP algorithm. As a result, the ramp filter and the windowing function are both modified by the Bayesian component. This new FBP algorithm can be applied to a projection data set that is not uniformly sampled.Results: Computer simulations show that the new FBP-MAP algorithm with window function index k and the iterative Landweber MAP algorithm with iteration number k give similar reconstructions in terms of resolution and noise texture. An example of transmission x-ray CT shows that the noise modeling method is able to significantly reduce the streaking artifacts associated with low-dose CT.Conclusions: View-based noise weighting scheme can be introduced to the FBP algorithm as a weighting factor in the window function. The new FBP algorithm is able to provide similar results to the iterative MAP algorithm if the ramp filter is modified with a additive term. Nonuniform sampling and sensitivity can be accommodated by proper backprojection weighting. (C) 2012 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.3697736]