Method to estimate fan‐beam CT noise power spectrum using two basis functions with a limited number of noise realizations

Abstract

Purpose The noise power spectrum (NPS) plays a key role in image quality (IQ) evaluation as it can be used for predicting detection performance or calculating detective quantum efficiency (DQE). Traditionally, the NPS is estimated by ensemble averaging multiple realizations of noise‐only images. However, the estimation error increases when there are a limited number of images. Since the estimation error directly affects the image quality (IQ) index, an accurate NPS estimation method is required. Recent works have proposed NPS estimation methods using the radial one‐dimensional (1D) NPS as the basis; however, when sharp kernels are used during image reconstruction, these methods cannot accurately estimate the amplitude of each angular spoke of the 2D NPS composed of different cutoff frequencies determined from the complementary projection magnification factors for different spatial regions. In this work, we propose a 2D NPS estimation method that reflects the accurate amplitude of each angular spoke for fan‐beam CT images. Methods An angular spoke of the 2D NPS is composed of two basis functions with different cutoff frequencies determined from the complementary projection magnification factors. The proposed method estimates these two weighting factors for each basis function by minimizing the mean‐squared error (MSE) between the 2D NPS estimated from 10 noise realizations. Two noise profiles and two types of apodization filters (i.e., rectangular and Hanning) were used to reconstruct the noise‐only images. To examine the nonstationary noise property of fan‐beam CT images, the 2D NPS was estimated at three different local regions. The estimation accuracy of the proposed method was further improved by estimating the approximate weighting factors with sinusoidal functions, considering that the weighting factors vary slowly throughout the view angles. Regression orders of 1 to 4 were used during these estimations. The approximate weighting factors were then multiplied with each of the basis functions to estimate the 2D NPS. The normalized mean‐squared error (NMSE) was used as an index to compare the performance of each NPS estimation method, with the analytical 2D NPS as the reference. Further validation was performed using XCAT phantom data. Results We observed that the 2D NPS estimated using two basis functions reflected the accurate amplitude of each angular spoke, whereas the 2D NPS estimated using the radial 1D NPS as the basis could not. The 2D NPS estimated by applying the approximate weighting factors showed improved performance compared with that estimated using two basis functions. In addition, unlike the view‐independent noise cases, where a lower regression order showed higher estimation performance, a higher regression order showed higher estimation performance in the view‐dependent noise cases. Conclusions In this work, we propose a 2D NPS estimation method that reflects the accurate amplitude of each angular spoke for fan‐beam CT images using two basis functions. We observed that the proposed ...

[Retracted] A Spatial Spectrum Estimation Method for Optimization and Improvement of Resource Allocation and Management of Public Sport and Health Facilities

“…In the process of public sport facility resource management, it is assumed that the configuration and management set G =( n , e ), N represents the node set of any public sport facility resource, and E represents the association number set in the public sport facility resource. Any public sport facility resource N is composed of n node spaces, which can also be expressed N =set( n 1 ,…, n n ) as belonging to any natural number [ 16 ]. E is composed of m associations, which can be expressed E =set{ e 1 ,…, e m } and n ∈ M belongs to any natural number.…”