Gang G J, Stayman J W, Zbijewski W, Siewerdsen J H
Department of Biomedical Engineering, Johns Hopkins University, Baltimore MD, USA 21205.
Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON, Canada M5G 2M9.
Proc SPIE Int Soc Opt Eng. 2013 Feb;8668. doi: 10.1117/12.2008408. Epub 2013 Mar 19.
Nonstationarity of CT noise presents a major challenge to the assessment of image quality. This work presents models for imaging performance in both filtered backprojection (FBP) and penalized likelihood (PL) reconstruction that describe not only the dependence on the imaging chain but also the dependence on the object as well as the nonstationary characteristics of the signal and noise. The work furthermore demonstrates the ability to impart control over the imaging process by adjusting reconstruction parameters to exploit nonstationarity in a manner advantageous to a particular imaging task.
A cascaded systems analysis model was used to model the local noise-power spectrum (NPS) and modulation transfer function (MTF) for FBP reconstruction, with locality achieved by separate calculation of fluence and system gain for each view as a function of detector location. The covariance and impulse response function for PL reconstruction (quadratic penalty) were computed using the implicit function theorem and Taylor expansion. Detectability index was calculated under the assumption of local stationarity to show the variation in task-dependent image quality throughout the image for simple and complex, heterogeneous objects. Control of noise magnitude and correlation was achieved by applying a spatially varying roughness penalty in PL reconstruction in a manner that improved overall detectability.
The models provide a foundation for task-based imaging performance assessment in FBP and PL image reconstruction. For both FBP and PL, noise is anisotropic and varies in a manner dependent on the path length of each view traversing the object. The anisotropy in turn affects task performance, where detectability is enhanced or diminished depending on the frequency content of the task relative to that of the NPS. Spatial variation of the roughness penalty can be exploited to control noise magnitude and correlation (and hence detectability).
Nonstationarity of image noise is a significant effect that can be modeled in both FBP and PL image reconstruction. Prevalent spatial-frequency-dependent metrics of spatial resolution and noise can be analyzed under assumptions of local stationarity, providing a means to analyze imaging performance as a function of location throughout the image. Knowledgeable selection of a spatially-varying roughness penalty in PL can potentially improve local noise and spatial resolution in a manner tuned to a particular imaging task.
CT噪声的非平稳性给图像质量评估带来了重大挑战。这项工作提出了滤波反投影（FBP）和惩罚似然（PL）重建中成像性能的模型，这些模型不仅描述了对成像链的依赖性，还描述了对物体的依赖性以及信号和噪声的非平稳特性。此外，该工作还展示了通过调整重建参数来控制成像过程的能力，以便以有利于特定成像任务的方式利用非平稳性。
使用级联系统分析模型对FBP重建的局部噪声功率谱（NPS）和调制传递函数（MTF）进行建模，通过根据探测器位置分别计算每个视图的注量和系统增益来实现局部性。使用隐函数定理和泰勒展开计算PL重建（二次惩罚）的协方差和脉冲响应函数。在局部平稳性假设下计算可探测性指数，以显示简单和复杂的异质物体在整个图像中与任务相关的图像质量变化。通过在PL重建中应用空间变化的粗糙度惩罚来控制噪声幅度和相关性，从而提高整体可探测性。
这些模型为FBP和PL图像重建中基于任务的成像性能评估提供了基础。对于FBP和PL，噪声都是各向异性的，并且以依赖于每个视图穿过物体的路径长度的方式变化。这种各向异性反过来又会影响任务性能，其中可探测性会根据任务的频率内容相对于NPS的频率内容而增强或减弱。可以利用粗糙度惩罚的空间变化来控制噪声幅度和相关性（从而控制可探测性）。
图像噪声的非平稳性是一个显著影响因素，在FBP和PL图像重建中均可进行建模。在局部平稳性假设下，可以分析普遍存在的与空间频率相关的空间分辨率和噪声指标，从而提供一种在整个图像中分析成像性能随位置变化的方法。在PL中明智地选择空间变化的粗糙度惩罚可能会以针对特定成像任务进行调整的方式潜在地改善局部噪声和空间分辨率。
