Noise-resolution tradeoffs in x-ray CT imaging: A comparison of penalized alternating minimization and filtered backprojection algorithms
Noise-resolution tradeoffs in x-ray CT imaging: A comparison of penalized alternating minimization and filtered backprojection algorithms
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DOI：
10.1118/1.3549757
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发表时间：
2011-03-01
期刊：
影响因子：
3.8
通讯作者：
Williamson, Jeffrey F.
中科院分区：
文献类型：
--
作者：
Evans, Joshua D.;Politte, David G.;Williamson, Jeffrey F.
目的：与用于X射线计算机断层摄影（CT）图像重建的常规滤波反投影（FBP）算法相比，统计算法直接结合数据的随机性质，并且不假设CT数据是衰减线积分的线性、无噪声函数。因此，已经假设统计图像重建可以在剂量受限的应用中在图像噪声和空间分辨率之间支持比FBP更有利的折衷。本研究的目的是评估交替最小化（AM）算法正则化使用nonquadratic penalty function.Methods：理想化的单能CT投影数据与泊松噪声的噪声分辨率权衡模拟两个phanteries与插入不同的对比度（7%-238%）和距离的视野（FOV）中心（2-6.5 cm）。利用FBP算法和惩罚AM算法的两个惩罚函数参数值对模拟投影数据进行图像重建。每种算法都使用一系列平滑强度运行，以量化噪声分辨率权衡曲线。图像噪声被量化为每个对比插入物周围的水背景中的标准偏差。调制传递函数（MTF）的计算从六参数模型拟合过采样边缘扩展函数定义的圆形对比度插入边缘作为局部分辨率的度量。结果：惩罚后的AM算法噪声-分辨率折衷曲线总是优于FBP算法。虽然发现分辨率和噪声对于两种算法不同地作为与FOV中心的距离的函数而变化，但是当匹配分辨率度量时，噪声的比率在图像上相对均匀。AM-到-FBP图像方差的比率，剂量降低潜力的预测因子，强烈依赖于AM的非二次罚函数的形状，并且也强烈地受到插入物的分辨率被量化的对比度的影响。对于AM算法的一个惩罚参数值，剂量降低潜力（此处报告为AM重建具有可比噪声和分辨率的图像所需的FBP剂量的分数（%））对于低对比度和高对比度结构分别为70%至50%，对于第二个AM惩罚参数值为70%至10%。然而，第二个惩罚，AM-700，被发现遭受低对比度分辨率差匹配时，高对比度分辨率度量与FBP.Conclusions：本模拟研究的结果意味着，惩罚AM有可能重建图像具有类似的噪声和分辨率使用分数（10%-70%）的FBP剂量。然而，这种剂量降低的潜力强烈地依赖于AM惩罚参数和感兴趣的结构的对比度大小。此外，作者的研究结果表明，AM的优势可以通过优化非二次罚函数的特定成像任务的兴趣。未来的工作将扩展这里使用的方法来量化从真实的CT数据重建的图像中的噪声和分辨率。(C)2011年美国医学物理学家协会。[DOI 10.1118/1.3549757]
Purpose: In comparison with conventional filtered backprojection (FBP) algorithms for x-ray computed tomography (CT) image reconstruction, statistical algorithms directly incorporate the random nature of the data and do not assume CT data are linear, noiseless functions of the attenuation line integral. Thus, it has been hypothesized that statistical image reconstruction may support a more favorable tradeoff than FBP between image noise and spatial resolution in dose-limited applications. The purpose of this study is to evaluate the noise-resolution tradeoff for the alternating minimization (AM) algorithm regularized using a nonquadratic penalty function.Methods: Idealized monoenergetic CT projection data with Poisson noise were simulated for two phantoms with inserts of varying contrast (7%-238%) and distance from the field-of-view (FOV) center (2-6.5 cm). Images were reconstructed for the simulated projection data by the FBP algorithm and two penalty function parameter values of the penalized AM algorithm. Each algorithm was run with a range of smoothing strengths to allow quantification of the noise-resolution tradeoff curve. Image noise is quantified as the standard deviation in the water background around each contrast insert. Modulation transfer functions (MTFs) were calculated from six-parameter model fits to oversampled edge-spread functions defined by the circular contrast-insert edges as a metric of local resolution. The integral of the MTF up to 0.5 lp/mm was adopted as a single-parameter measure of local spatial resolution.Results: The penalized AM algorithm noise-resolution tradeoff curve was always more favorable than that of the FBP algorithm. While resolution and noise are found to vary as a function of distance from the FOV center differently for the two algorithms, the ratio of noises when matching the resolution metric is relatively uniform over the image. The ratio of AM-to-FBP image variances, a predictor of dose-reduction potential, was strongly dependent on the shape of the AM's nonquadratic penalty function and was also strongly influenced by the contrast of the insert for which resolution is quantified. Dose-reduction potential, reported here as the fraction (%) of FBP dose necessary for AM to reconstruct an image with comparable noise and resolution, for one penalty parameter value of the AM algorithm was found to vary from 70% to 50% for low-contrast and high-contrast structures, respectively, and from 70% to 10% for the second AM penalty parameter value. However, the second penalty, AM-700, was found to suffer from poor low-contrast resolution when matching the high-contrast resolution metric with FBP.Conclusions: The results of this simulation study imply that penalized AM has the potential to reconstruct images with similar noise and resolution using a fraction (10%-70%) of the FBP dose. However, this dose-reduction potential depends strongly on the AM penalty parameter and the contrast magnitude of the structures of interest. In addition, the authors' results imply that the advantage of AM can be maximized by optimizing the nonquadratic penalty function to the specific imaging task of interest. Future work will extend the methods used here to quantify noise and resolution in images reconstructed from real CT data. (C) 2011 American Association of Physicists in Medicine. [DOI: 10.1118/1.3549757]