Department of Bio-Industrial Mechatronics Engineering, National Taiwan University, 1, Section 4, Roosevelt Road, Taipei, Taiwan 106, Taiwan.
Med Phys. 2010 Jan;37(1):270-81. doi: 10.1118/1.3267548.
X-ray phase-contrast tomography (PCT) is a rapidly emerging imaging modality for reconstructing estimates of an object's three-dimensional x-ray refractive index distribution. Unlike conventional x-ray computed tomography methods, the statistical properties of the reconstructed images in PCT remain unexplored. The purpose of this work is to quantitatively investigate noise propagation in PCT image reconstruction.
The authors derived explicit expressions for the autocovariance of the reconstructed absorption and refractive index images to characterize noise texture and understand how the noise properties are influenced by the imaging geometry. Concepts from statistical detection theory were employed to understand how the imaging geometry-dependent statistical properties affect the signal detection performance in a signal-known-exactly/background-known-exactly task.
The analytical formulas for the phase and absorption autocovariance functions were implemented numerically and compared to the corresponding empirical values, and excellent agreement was found. They observed that the reconstructed refractive images are highly spatially correlated, while the absorption images are not. The numerical results confirm that the strength of the covariance is scaled by the detector spacing. Signal detection studies were conducted, employing a numerical observer. The detection performance was found to monotonically increase as the detector-plane spacing was increased.
The authors have conducted the first quantitative investigation of noise propagation in PCT image reconstruction. The reconstructed refractive images were found to be highly spatially correlated, while absorption images were not. This is due to the presence of a Fourier space singularity in the reconstruction formula for the refraction images. The statistical analysis may facilitate the use of task-based image quality measures to further develop and optimize this emerging modality for specific applications.
X 射线相衬断层摄影术（PCT）是一种新兴的成像方式，可用于重建物体三维 X 射线折射率分布的估计值。与传统的 X 射线计算机断层摄影方法不同，PCT 中重建图像的统计特性仍未得到探索。本研究旨在定量研究 PCT 图像重建中的噪声传播。
作者推导出了重建的吸收和折射率图像的自协方差的显式表达式，以描述噪声纹理，并了解噪声特性如何受到成像几何形状的影响。采用统计检测理论中的概念来理解成像几何形状相关的统计特性如何影响信号已知/背景已知的任务中的信号检测性能。
相位和吸收自协方差函数的解析公式已通过数值实现，并与相应的经验值进行了比较，结果吻合得非常好。他们发现，重建的折射率图像具有高度的空间相关性，而吸收图像则没有。数值结果证实，协方差的强度与探测器间距成比例。采用数值观察者进行了信号检测研究。发现随着探测器平面间距的增加，检测性能呈单调递增。
作者对 PCT 图像重建中的噪声传播进行了首次定量研究。发现重建的折射率图像具有高度的空间相关性，而吸收图像则没有。这是由于在折射率图像的重建公式中存在傅里叶空间奇点。该统计分析可能有助于基于任务的图像质量度量的使用，以进一步开发和优化这种新兴模态以适应特定应用。
