Division of Imaging, Diagnostics, and Software Reliability, Office of Science and Engineering Laboratories, CDRH, FDA, Silver Spring, MD, 20993, USA.
The Computer Science Department, Stony Brook University, Stony Brook, NY, 11794, USA.
Med Phys. 2019 Apr;46(4):1634-1647. doi: 10.1002/mp.13428. Epub 2019 Feb 28.
For computed tomography (CT) systems in which noise is nonstationary, a local noise power spectrum (NPS) is often needed to characterize its noise property. We have previously developed a data-efficient radial NPS method to estimate the two-dimensional (2D) local NPS for filtered back projection (FBP)-reconstructed fan-beam CT utilizing the polar separability of CT NPS. In this work, we extend this method to estimate three-dimensional (3D) local NPS for feldkamp-davis-kress (FDK)-reconstructed cone-beam CT (CBCT) volumes.
Starting from the 2D polar separability, we analyze the CBCT geometry and FDK image reconstruction process to derive the 3D expression of the polar separability for CBCT local NPS. With the polar separability, the 3D local NPS of CBCT can be decomposed into a 2D radial NPS shape function and a one-dimensional (1D) angular amplitude function with certain geometrical transforms. The 2D radial NPS shape function is a global function characterizing the noise correlation structure, while the 1D angular amplitude function is a local function reflecting the varying local noise amplitudes. The 3D radial local NPS method is constructed from the polar separability. We evaluate the accuracy of the 3D radial local NPS method using simulated and real CBCT data by comparing the radial local NPS estimates to a reference local NPS in terms of normalized mean squared error (NMSE) and a task-based performance metric (lesion detectability).
In both simulated and physical CBCT examples, a very small NMSE (<5%) was achieved by the radial local NPS method from as few as two scans, while for the traditional local NPS method, about 20 scans were needed to reach this accuracy. The results also showed that the detectability-based system performances computed using the local NPS estimated with the NPS method developed in this work from two scans closely reflected the actual system performance.
The polar separability greatly reduces the data dimensionality of the 3D CBCT local NPS. The radial local NPS method developed based on this property is shown to be capable of estimating the 3D local NPS from only two CBCT scans with acceptable accuracy. The minimum data requirement indicates the potential utility of local NPS in CBCT applications even for clinical situations.
对于噪声非平稳的计算机断层扫描（CT）系统，通常需要局部噪声功率谱（NPS）来描述其噪声特性。我们之前开发了一种数据高效的径向 NPS 方法，用于利用 CT NPS 的极可分离性估计滤波反投影（FBP）重建的扇形束 CT 的二维（2D）局部 NPS。在这项工作中，我们将该方法扩展到用于 Feldkamp-Davis-Kress（FDK）重建的锥形束 CT（CBCT）体积的三维（3D）局部 NPS 估计。
从 2D 极可分离性出发，我们分析了 CBCT 几何形状和 FDK 图像重建过程，得出了 CBCT 局部 NPS 的 3D 表达式。利用极可分离性，可以将 CBCT 的 3D 局部 NPS 分解为具有一定几何变换的 2D 径向 NPS 形状函数和 1D 角振幅函数。2D 径向 NPS 形状函数是一个全局函数，用于描述噪声相关结构，而 1D 角振幅函数是反映局部噪声幅度变化的局部函数。3D 径向局部 NPS 方法是从极可分离性构建的。我们使用模拟和真实的 CBCT 数据来评估 3D 径向局部 NPS 方法的准确性，通过比较径向局部 NPS 估计值与参考局部 NPS 在归一化均方误差（NMSE）和基于任务的性能指标（病灶检测）方面的差异来评估。
在模拟和物理 CBCT 示例中，径向局部 NPS 方法仅使用两到三个扫描即可获得非常小的 NMSE（<5%），而传统的局部 NPS 方法则需要大约 20 个扫描才能达到这种精度。结果还表明，使用本文开发的 NPS 方法从两个扫描中估计的局部 NPS 计算的基于检测的系统性能与实际系统性能非常接近。
极可分离性大大降低了 3D CBCT 局部 NPS 的数据维数。基于该特性开发的径向局部 NPS 方法被证明能够仅使用两个 CBCT 扫描以可接受的精度估计 3D 局部 NPS。最小的数据要求表明局部 NPS 在 CBCT 应用中的潜在效用，即使在临床情况下也是如此。
