Two-Dimensional Tomography from Noisy Projections Taken at Unknown Random Directions.
Two-Dimensional Tomography from Noisy Projections Taken at Unknown Random Directions.
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DOI：
10.1137/090764657
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发表时间：
2013-01-01
影响因子：
2.1
通讯作者：
Wu HT
中科院分区：
文献类型：
--
作者：
Singer A;Wu HT
计算机断层扫描是从物体的投影图像中获得物体内部结构的一种标准方法。虽然CT重建需要知道成像方向，但在某些情况下，成像方向是未知的，例如对运动物体进行成像。因此，需要从在未知方向拍摄的投影图像设计一种重建方法。另一个困难来自这样一个事实，即预测经常受到噪声的污染，实际上限制了所有当前的方法，包括最近提出的扩散图方法。在本文中，我们引入了两个去噪步骤，当与扩散图框架相结合时，它们允许以更低的信噪比（SNRs）重建。在去噪的第一步，我们使用主成分分析（PCA）和经典维纳滤波来推导渐近最优线性滤波器。在第二步中，我们使用网络分析度量（如Jaccard指数）对过滤后的投影之间的相似性图进行降噪。使用PCA、Wiener滤波、图去噪和扩散图的组合，我们能够在远低于目前报道的阈值的信噪比下，从模拟噪声投影中重建二维（2-D） Shepp-Logan幻像。我们还报告了与腹部CT相对应的数值实验结果。虽然本文的重点是二维CT重建问题，但我们相信PCA、维纳滤波、图去噪和扩散图的结合在其他信号处理和图像分析应用中是潜在的有用的。
Computerized tomography is a standard method for obtaining internal structure of objects from their projection images. While CT reconstruction requires the knowledge of the imaging directions, there are some situations in which the imaging directions are unknown, for example, when imaging a moving object. It is therefore desirable to design a reconstruction method from projection images taken at unknown directions. Another difficulty arises from the fact that the projections are often contaminated by noise, practically limiting all current methods, including the recently proposed diffusion map approach. In this paper, we introduce two denoising steps that allow reconstructions at much lower signal-to-noise ratios (SNRs) when combined with the diffusion map framework. In the first denoising step we use principal component analysis (PCA) together with classical Wiener filtering to derive an asymptotically optimal linear filter. In the second step, we denoise the graph of similarities between the filtered projections using a network analysis measure such as the Jaccard index. Using this combination of PCA, Wiener filtering, graph denoising, and diffusion maps, we are able to reconstruct the two-dimensional (2-D) Shepp–Logan phantom from simulative noisy projections at SNRs well below their currently reported threshold values. We also report the results of a numerical experiment corresponding to an abdominal CT. Although the focus of this paper is the 2-D CT reconstruction problem, we believe that the combination of PCA, Wiener filtering, graph denoising, and diffusion maps is potentially useful in other signal processing and image analysis applications.
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