“…9,10 Many NPS studies have been conducted in the past to assess the noise characteristics of clinical CT systems. [11][12][13] Traditionally, the NPS is estimated by ensemble averaging multiple realizations of noise-only images. 14 However, the estimation error increases when there are a limited number of images.…”
Section: Introductionmentioning
confidence: 99%
“…The NPS plays a key role in image quality (IQ) evaluation as it can be used for predicting detection performance 6–8 or calculating detective quantum efficiency (DQE) 9,10 . Many NPS studies have been conducted in the past to assess the noise characteristics of clinical CT systems 11–13 …”
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 ...
“…9,10 Many NPS studies have been conducted in the past to assess the noise characteristics of clinical CT systems. [11][12][13] Traditionally, the NPS is estimated by ensemble averaging multiple realizations of noise-only images. 14 However, the estimation error increases when there are a limited number of images.…”
Section: Introductionmentioning
confidence: 99%
“…The NPS plays a key role in image quality (IQ) evaluation as it can be used for predicting detection performance 6–8 or calculating detective quantum efficiency (DQE) 9,10 . Many NPS studies have been conducted in the past to assess the noise characteristics of clinical CT systems 11–13 …”
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 ...
“…Generally, performance of the imaging diagnostic system is calibrated with three main technical specifications: the modulation transfer function (MTF) [4], the noise power spectrum (NPS) [5] [6], and the detective quantum efficiency (DQE) [7] [8]. MTF is a universally accepted standard to calibrate the spatial resolution of the system.…”
The diagnostic methods for the profile of the radiation source were established at first based on the pinhole imaging principle. In this paper, the relationships among various parameters of the gamma-rays crammer such as the modulation transfer function (MTF), the noise power spectrum (NPS), the signal-noise ratio (SNR) and the detective quantum efficiency (DQE) are developed and studied experimentally on the cobalt radiation source. The image diagnostic system is consisting with rays-fluorescence convertor (YAG crystal), optical imaging system, MCP image intensifier, CCD camera and other devices. The spatial resolution of the modulation transfer function (MTF) at 10% intensity was measured as 1 lp/mm by knife-edge method. The quantum of the measurement system is about 150 under weak radiation condition due to the single particle detection efficiency of the system. The dynamic range was inferred preliminarily as about 437. The required radiation intensity was calculated using the experiment result for the SNR = 1, 5, 10, respectively. The theoretical investigation results show that the radiation image with SNR = 1 can be only obtained when the pinhole diameter is 0.7 mm, object distance and image distance are both 200 cm, and the radiation intensity is about 1.0 × 10 12 Sr −1 ⋅cm −2 .
The state of the art to describe image quality in medical imaging is to assess the performance of an observer conducting a task of clinical interest. This can be done by using a model observer leading to a figure of merit such as the signal-to-noise ratio (SNR). Using the non-prewhitening (NPW) model observer, we objectively characterised the evolution of its figure of merit in various acquisition conditions. The NPW model observer usually requires the use of the modulation transfer function (MTF) as well as noise power spectra. However, although the computation of the MTF poses no problem when dealing with the traditional filtered back-projection (FBP) algorithm, this is not the case when using iterative reconstruction (IR) algorithms, such as adaptive statistical iterative reconstruction (ASIR) or model-based iterative reconstruction (MBIR). Given that the target transfer function (TTF) had already shown it could accurately express the system resolution even with non-linear algorithms, we decided to tune the NPW model observer, replacing the standard MTF by the TTF. It was estimated using a custom-made phantom containing cylindrical inserts surrounded by water. The contrast differences between the inserts and water were plotted for each acquisition condition. Then, mathematical transformations were performed leading to the TTF. As expected, the first results showed a dependency of the image contrast and noise levels on the TTF for both ASIR and MBIR. Moreover, FBP also proved to be dependent of the contrast and noise when using the lung kernel. Those results were then introduced in the NPW model observer. We observed an enhancement of SNR every time we switched from FBP to ASIR to MBIR. IR algorithms greatly improve image quality, especially in low-dose conditions. Based on our results, the use of MBIR could lead to further dose reduction in several clinical applications.
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