Zeng Rongping, Gavrielides Marios A, Petrick Nicholas, Sahiner Berkman, Li Qin, Myers Kyle J
Division of Imaging, Diagnostics, and Software Reliability, Office of Science and Engineering Laboratories, CDRH, FDA, Silver Spring, Maryland 20993.
Med Phys. 2016 Jan;43(1):568. doi: 10.1118/1.4939061.
Traditional ways to estimate 2D CT noise power spectrum (NPS) involve an ensemble average of the power spectrums of many noisy scans. When only a few scans are available, regions of interest are often extracted from different locations to obtain sufficient samples to estimate the NPS. Using image samples from different locations ignores the nonstationarity of CT noise and thus cannot accurately characterize its local properties. The purpose of this work is to develop a method to estimate local NPS using only a few fan-beam CT scans.
As a result of FBP reconstruction, the CT NPS has the same radial profile shape for all projection angles, with the magnitude varying with the noise level in the raw data measurement. This allows a 2D CT NPS to be factored into products of a 1D angular and a 1D radial function in polar coordinates. The polar separability of CT NPS greatly reduces the data requirement for estimating the NPS. The authors use this property and derive a radial NPS estimation method: in brief, the radial profile shape is estimated from a traditional NPS based on image samples extracted at multiple locations. The amplitudes are estimated by fitting the traditional local NPS to the estimated radial profile shape. The estimated radial profile shape and amplitudes are then combined to form a final estimate of the local NPS. We evaluate the accuracy of the radial NPS method and compared it to traditional NPS methods in terms of normalized mean squared error (NMSE) and signal detectability index.
For both simulated and real CT data sets, the local NPS estimated with no more than six scans using the radial NPS method was very close to the reference NPS, according to the metrics of NMSE and detectability index. Even with only two scans, the radial NPS method was able to achieve a fairly good accuracy. Compared to those estimated using traditional NPS methods, the accuracy improvement was substantial when a few scans were available.
The radial NPS method was shown to be accurate and efficient in estimating the local NPS of FBP-reconstructed 2D CT images. It presents strong advantages over traditional NPS methods when the number of scans is limited and can be extended to estimate the in-plane NPS of cone-beam CT and multislice helical CT scans.
传统的估计二维CT噪声功率谱（NPS）的方法需要对许多噪声扫描的功率谱进行总体平均。当只有少数扫描可用时，通常会从不同位置提取感兴趣区域以获得足够的样本用于估计NPS。使用来自不同位置的图像样本会忽略CT噪声的非平稳性，因此无法准确表征其局部特性。这项工作的目的是开发一种仅使用少数扇束CT扫描来估计局部NPS的方法。
由于滤波反投影（FBP）重建，CT NPS对于所有投影角度具有相同的径向轮廓形状，其幅度随原始数据测量中的噪声水平而变化。这使得二维CT NPS能够在极坐标中分解为一维角度函数和一维径向函数的乘积。CT NPS的极坐标可分离性大大降低了估计NPS的数据要求。作者利用这一特性推导了一种径向NPS估计方法：简而言之，从基于在多个位置提取的图像样本的传统NPS估计径向轮廓形状。通过将传统局部NPS拟合到估计的径向轮廓形状来估计幅度。然后将估计的径向轮廓形状和幅度组合起来形成局部NPS的最终估计值。我们评估了径向NPS方法的准确性，并在归一化均方误差（NMSE）和信号可检测性指数方面将其与传统NPS方法进行了比较。
对于模拟和真实CT数据集，根据NMSE和可检测性指数指标，使用径向NPS方法用不超过六次扫描估计的局部NPS与参考NPS非常接近。即使只有两次扫描，径向NPS方法也能够实现相当好的准确性。与使用传统NPS方法估计的结果相比，当有少数扫描可用时，准确性有显著提高。
径向NPS方法在估计FBP重建的二维CT图像的局部NPS方面被证明是准确且高效的。当扫描次数有限时，它相对于传统NPS方法具有显著优势，并且可以扩展到估计锥束CT和多层螺旋CT扫描的面内NPS。
