Automated measurement of CT noise in patient images with a novel structure coherence feature

Computed tomography (CT) has been established as a fundamental modality in the daily practice of patient care (Brenner and Hall 2007). CT examinations were performed more than 85 million times in the United States in 2011 (Miglioretti et al 2013), which is increasing at around 10% each year (Schauer and Linton 2009). On the other hand, concern about the radiation exposure associated with CT examinations is also growing. A recent report suggests that even a low-level exposure of ionizing radiation such as that from CT examinations could lead to the development of cancer (National Research Council 2006, Smith-Bindman et al 2012). Therefore, efforts have been made to reduce the radiation dose while maintaining the image quality by optimizing CT protocols based on the as low as reasonably achievable (ALARA) principle in a variety of directions including the evaluation of automatic exposure control (AEC), iterative reconstruction, adaptive kVp selection, and dual energy (DE)-based virtual monochromatic imaging (Kalra et al 2004, Smith-Bindman et al 2009, Prakash et al 2010, Yu et al 2010, 2012).

Any of these studies requires the assessment of a certain image quality metric in order to assess if a given technique is maintaining the image quality while reducing the radiation dose ALARA. Noise as assessed with the standard deviation of CT number within an ROI is the most commonly used metric for image quality assessment in CT, which also constitutes a core feature in assessing other image quality metrics such as signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) (AAPM et al 1977). Often the mean signal or contrast of reference tissue is known previously and does not change sensitively according to the parameters: Noise is the primary variable determining the image quality (Schuhbaeck et al 2013). Therefore, the reliable and efficient measurement of noise forms a primary basis for the tasks of the image quality assessment of CT for further technical developments and the patient specific optimization of scan parameters (Menzel et al 2000).

Despite the importance of the noise measurement, however, studies still depend on manual work for determining the homogeneous region and placing ROIs (Christe et al 2013). Manual measurements of noise require the determination of the homogeneous region as well as the placement of ROIs with adequate size, which involves perceptual subjectivity and the eye-hand coordination of a rater, and in turn unavoidably introduces rater variability and bias to the noise measurements. Moreover, the inefficiency of manual measurement is not able to cope with the massive workload required in studies to investigate or carry out surveillance on noise profiles across hundreds of slices according to the different CT parameters. This calls for the need to develop a computer-assisted method for the reliable and efficient measurement of noise on CT images. However, an automated method for noise measurement in patient CT images has rarely been studied to date. Only recently, Christianson et al proposed an automated method for measuring the global CT noise based on a noise histogram, although their ROI placement contained a small-scale anatomical structure resulting in an over-estimation of the noise level (Christianson et al 2015).

Therefore, the purpose of this study is to develop a fully automated CT noise level measurement algorithm which can be used for the high throughput assessment of the image quality metrics of CT scans in studies investigating the optimization of scan protocols. In this paper, we describe our novel feature to discriminate a homogeneous ROI from structural signals, and present a procedure to automate the selection of reference tissue, the extraction of feature, the determination of representative ROIs, and noise level assessment. In addition, we provide the results of an experiment evaluating the performance of our proposed algorithm by two radiologists.

2.1. CT dataset

2.2. Structure coherence feature

The key to success in automated noise measurement on CT images is determining the homogeneous ROIs, which are usually defined by the absence of any visible anatomical structure within an ROI. Determining homogeneous ROIs on noisy CT images, however, is not an easy task. Discriminating anatomical structures from background noise is often ambiguous because the amount of noise is comparable to or greater than subtle small-scale structures and varies across the pixel locations.

In this study, we devised a novel structure coherence feature f_s to effectively represent the likelihood of a pixel belonging to an anatomical structure. We employed two different features to represent structure coherence: An edginess feature to represent the likelihood of a pixel being located on an anatomical structure and the randomness of the pixel orientation to signify the absence of an anatomical structure. Shown in (1) is the formula combining these two features to define our composite feature for structure coherence f_s:

$$\begin{eqnarray}&&{{f}_{\text{s}}}=\frac{\underset{(i,j)\in \text{ROI}}{\mathop \sum}{{I}_{\text{E}}}(i,j)}{{{H}_{\text{G}}}+{{H}_{\text{T}}}},\end{eqnarray} \tag{ 1 }$$

where I_E denotes the edginess of each pixel. The randomness of the pixel orientation is represented by the sum of H_G and H_T, which denote the directional entropy values for the gradient vector and structure tensor, respectively.

We defined the edginess of a pixel by the weighted sum of the magnitudes for the gradient and the 1st eigenvalue of the structure tensor as (2). The edginess I_E was designed to represent two different types of edge in a balanced way: The transitional edge between distinct regions and the curvilinear edge caused by tubular structures such as blood vessels or ducts.

$$\begin{eqnarray}&&{{I}_{\text{E}}}={{\omega}_{1}}|\nabla I|\,+\,{{\omega}_{2}}|{{\lambda}_{1}}|.\end{eqnarray} \tag{ 2 }$$

where $\nabla I$ and ${{\lambda}_{1}}$ denote the gradient and the 1st eigenvalue of the structure tensor of the given image, and the corresponding weights ${{\omega}_{1}}$ and ${{\omega}_{2}}$ were 0.75 and 0.25 to best represent both the transitional and curvilinear edges. The randomness of the pixel orientation was assessed within an ROI by summing the two directional entropy values (H_G, H_T) for the gradient vector and structure tensor (Baghaie and Yu 2015):

$$\begin{eqnarray}&&{{H}_{\text{G}}}=-\underset{(i,j)\in \text{ROI}}{\mathop \sum}P\left(\angle \nabla I\right)\text{ln}P\left(\angle \nabla I\right),\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{{H}_{\text{T}}}=-\underset{(i,j)\in \text{ROI}}{\mathop \sum}P\left(\angle {{V}_{\text{T}}}\right)\text{ln}P\left(\angle {{V}_{\text{T}}}\right),\end{eqnarray} \tag{ 4 }$$

where V_T was the 1st eigenvector of structure tensor T, which is defined as,

$$\begin{eqnarray}T=\left|\begin{array}{c} {{I}_{x}}^{2} & {{I}_{x}}{{I}_{y}} \\ {{I}_{x}}{{I}_{y}} & {{I}_{y}}^{2} \end{array}\right|=\left|\begin{array}{c} {{T}_{11}} & {{T}_{12}} \\ {{T}_{12}} & {{T}_{22}} \end{array}\right|,\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{{V}_{T}}=\left(\begin{array}{c} {{T}_{22}}-{{T}_{11}}+\sqrt{{{\left({{T}_{22}}-{{T}_{11}}\right)}^{2}}+4{{T}_{12}}^{2}} \\ -2{{T}_{12}} \end{array}\right).\end{eqnarray} \tag{ 6 }$$

Figure 1 shows the characteristics of the proposed structure coherence feature and its sub-components for typical ROIs in homogeneous and structural regions in an example CT image.

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Shown in figure 2 are the distribution of the edginess, the randomness of the pixel orientation, and the structure coherence feature values mapped on an example CT image. Although the edginess and pixel orientation features provide a distinction between the homogeneous and structural regions to a degree, their composite, a structure coherence feature, improves the distinction markedly.

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2.3. Automated noise measurement procedure

2.3.1. Overall procedure.

The schematic diagram of the overall procedure for the proposed automated noise measurement algorithm is shown in figure 3. The procedure begins with the segmentation of the reference tissue, which was fat in this study. Following this are the calculation of the structure coherence feature at each pixel and the determination of ROIs in the homogeneous region based on the structure coherence feature. Finally, the noise level was assessed by averaging the standard deviation of HU within an ROI for the 5 randomly selected ROIs for a given image.

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2.3.2. Segmentation of fat tissue.

A CT image contains several types of tissue, and the noise level varies depending upon the tissue type. Therefore, the first step in noise level assessment is to select a reference tissue. We chose fat as a reference tissue in this study because of the relatively abundant amount of fat tissue existing along the z-axis throughout the entire body compared to other tissues. Also, fat has a unique Hounsfield unit (HU) range from  −150 to  −30 HU, which makes it relatively straightforward to segment the fat area (Popuri et al 2013, Padgett et al 2014).

As a preprocess, we carried out Gaussian filtering on the CT images to reduce the effect of noise on fat mask generation. This was followed by thresholding with a lower bound of −150 HU and an upper bound of  −30 HU. Then we performed a test to find out if a given CT image contained a sufficient amount of fat tissue to place multiple ROIs. A morphology closing operation was performed with a structuring element size of 7 pixels, and we checked if the number of remaining pixels was less than a heuristically predetermined threshold. If it was smaller than the threshold, then the given CT image was considered as not appropriate for noise assessment and we skipped to the next slice image. Figure 4 shows the fat tissue selection procedure.

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2.3.3. Determination of representative ROIs.

In this study, we used a circle-shaped ROI with an area less than 1 cm². We followed the recommendation of the AAPM 39 Reports guideline in determining the suitable ROI size that provides reliable statistics and fits most of the homogeneous regions (AAPM TG-2 1993). In order to further reduce the variation of noise measurements at each ROI, we selected 5 representative ROIs among those ROIs placed within the segmented fat mask. First, the ROIs were placed at every pixel within the segmented fat mask, and f_s was extracted for each ROI according to equation (1). Then a histogram of f_s was created, and the f_s value of the 10th percentile was used as a threshold to choose homogeneous ROIs with as small structural patterns as possible. Finally, we randomly selected 5 ROIs among the chosen homogeneous ROIs. Shown in figure 5 are an example histogram of f_s, the selected homogeneous ROIs with f_s less than the 10th percentile, and the 5 randomly selected ROIs. The success or failure of the representative ROI placements was determined by an experienced reader with more than 5 years of CT image processing and was recorded to calculate the success rate of the ROI placement. The ROI placements made within the homogeneous fat region were regarded as successful, while those placed on structural patterns was regarded as failures.

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2.3.4. Assessment of image noise.

The 5 representative ROIs were then utilized for an assessment of the noise level at a given image. The standard deviation of each localized ROI was calculated by using,

$$\begin{eqnarray}&&{{\sigma}_{i}}={{\left[\frac{1}{N}\underset{k}{\overset{{}}{\mathop \sum}}{{\left({{x}_{k}}-\overline{x}\right)}^{2}}\right]}^{1/2}}.\end{eqnarray} \tag{ 7 }$$

In order to obtain more reliable measurements, the noise level as assessed by our automated algorithm was obtained by averaging the standard deviations for the 5 ROIs as,

$$\begin{eqnarray}&&{{\sigma}_{\text{A}}}=\frac{1}{5}\underset{i=1}{\overset{5}{\mathop \sum}}{{\sigma}_{i}}.\end{eqnarray} \tag{ 8 }$$

2.4. Validation of automated noise measurements

2.4.1. Comparison with the experts' manual noise measurements.

For a comparison of the noise measurements by the proposed algorithm with those by the experts, 2 radiologists (experience of 11 and 5 years) participated in this study. They were requested to measure the noise level for 100 subset images by manually drawing an ROI per slice with the guidance of setting the ROIs to be placed on most homogeneous fat regions with an area less than 1 cm². The ImageJ software program was used for the manual noise measurements.

The manual measurements were carried out repeatedly twice by rater_A, and a single manual measurement was made by rater_B. The first measurement of rater_A and the measurement of rater_B was averaged and used as the reference noise level (${{\sigma}_{\text{ref}}}$). The within-rater reliability of the experts' manual noise measurement was assessed with the Pearson correlation coefficient between the repeated measurements of rater_A, whereas the between-rater reliability was assessed with the Pearson correlation coefficient between the first measurement of rater_A and the measurement of rater_B. The variability of the manual noise measurements was assessed with the standard deviation of differences in noise measurements for within and between readers.

2.4.2. Validation with simulated low-dose CT.

We randomly selected 100 subset images from the low-dose CT data and created the corresponding simulated reduced-dose CT images at a 50% dose rate by applying a realistic reduced-dose CT simulation technique. This technique is based on a mathematical model, which reflects physical quantum statistic and the CT reconstruction process (Kim and Kim 2014). The technique enabled the generation of a realistic noise pattern appearing on low-dose CT images using sinogram synthesis and the filtered back projection of simulated noises. The used technique was validated previously at various reduced-dose levels, and has been shown to provide realistic noise patterns with regard to noise magnitude, texture, and streaks that were indistinguishable from that of a real CT system (Kim and Kim 2014). Example CT images of the 50% dose rate generated with the low-dose simulation technique are shown in comparison with the original image in figure 6. Noise level measurements by the proposed algorithm made on the 50% dose images were divided by those on the 100% dose images for each image pair to examine if the ratio of the noise level followed the theoretical value (1.414).

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2.4.3. Comparison of noise level across study groups.

The proposed algorithm was applied to all the CT datasets to assess the noise levels according to the 3 study groups (chest low-dose, chest routine, and abdominopelvic) for the pediatric and adult patients. The noise levels assessed at individual slices were averaged to yield the noise level of a study, and the noise levels of individual studies within a study group were in turn averaged to represent the noise level of a study group. The noise levels of the CT scans were compared between the different study groups, and between the pediatric and adult patients. In particular, a student t-test was applied to examine if there was a statistical difference in noise levels between the CT scans of the pediatric and adult patients for each study group.

2.5. Statistical analysis

3.1. Visual assessment

Typical examples of the visual assessment are shown in figure 7. In most cases, the proposed algorithm was able to localize the homogeneous regions and place 5 representative ROIs successfully across the different body parts and age groups used in this study. As shown in table 3, the overall success rate was 99.46% with a slightly higher success rate for the abdominopelvic scans (>99.7%) than for the chest scans (>98.4%). There was no appreciable difference in the success rate between the pediatric and adult patient groups. The cases of failure were found to contain strong streak artifacts due to photon starvation typically appearing around the shoulder in low-dose chest scans.

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Table 3. Comparison of the noise levels according to the study groups.

	Pediatrics			Adults
	Protocol A	Protocol B	Protocol C	Protocol A	Protocol B	Protocol C
Mean noise	6.9  ±  1.5	9.0  ±  2.1	7.5  ±  1.0	10.5  ±  1.9	14.8  ±  2.8	8.4  ±  1.4
Success rate (Success/total)	99.8% (1338/1341)	97.9% (2067/2111)	99.8% (4746/4752)	98.7% (1763/1786)	97.1% (668/688)	99.7% (5820/5839)

3.2. Comparison with the experts' manual noise measurements

The within-rater agreement for the repeated manual measurements was 0.75, and the between-rater agreement of the two radiologists was 0.70. These indicate the existence of a considerable discrepancy between measurements, which translates each noise measurement significantly depending on the raters and circumstances. Indeed, the within-rater and between-rater variability was 2.0 and 2.2 HU, respectively, which was around the 20% of the mean noise (10.37 HU). The agreement of the automated measurements with the reference noise measurements was 0.86, and the variability of the automated measurements against the reference noise measurements was 1.3 HU.

Shown in figure 8 are the scatter plots for the within and between-rater agreements as well as the agreement of the automated measurements with the reference noise measurements. The corresponding Bland–Altman plots are shown in figure 9 to assess the systemic bias and limits of agreement. No appreciable systemic bias was observed between the repeated noise measurements or the between noise measurements by the two radiologists. On the other hand, the automated noise measurements were systematically lower than the reference noise measurements (−1.56 HU, p  <  0.001). The reliability assessment results are summarized in table 4.

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Table 4. Reliability assessment results for the manual and automated noise measurements.

	Within-rater	Between-rater	Reference versus automated
Agreement (PCC)	0.75	0.70	0.86
Mean difference	−0.07 (p  =  0.726)	0.02 (p  =  0.93)	−1.56 (p  <  0.001)
Variability (standard deviation)	2.0	2.2	1.3
95% limits of agreement	[−3.985, 3.845]	[−4.306, 4.344]	[−4.195 1.070]

3.3. Validation with simulated low-dose CT

Figure 10(a) shows the noise level distribution for the original image set in comparison with those for the simulated reduced-dose image set and theoretical values. The mean  ±  standard deviation of the noise levels for the original image set were 12.69  ±  2.76 HU, whereas those for the simulated reduced-dose image set and the theoretical values were 17.87  ±  3.47 HU and 17.95  ±  3.91 HU, respectively, showing an excellent match between the measured and theoretical noise distributions. Figure 10(b) shows the ratio of the noise levels for the simulated reduced-dose image set to those for the original image set. The mean  ±  standard deviation ratio was 1.415  ±  0.089, which matched excellently the theoretical level of the 50% reduced-dose ($\sqrt{2}$).

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3.4. Comparison of noise levels across the study groups

This paper presents a fully automated noise measurement algorithm in patient CT images. We devised a novel structure coherence feature and developed a procedure that employed the structure coherence feature to distinguish homogeneous ROIs from those with structural patterns. By assessing the image noise with an average HU standard deviation on 5 representative ROIs, we could measure reliable noise levels in patient CT images in a fully automated way. In a performance evaluation experiment with patient CT cases of pediatric and adult patients, the proposed algorithm could successfully localize homogenous ROIs on 16 427 CT images out of a 16 517 test data set (99.46%), which appears to be sufficiently high success rate for use in practice.

Also, in an agreement test with 2 expert radiologists, the proposed algorithm was shown to agree excellently (r  =  0.86) with the reference measurements. In particular, the agreement of the proposed algorithm with the reference measurements was appreciably higher than the within-rater (r  =  0.75) and between-rater (r  =  0.70) agreements of the expert radiologists participating in this study. In addition, in a validation study with the simulated reduced-dose images, the noise measurements by the proposed algorithm matched excellently the theoretical values. Overall, our study results appear to suggest that the proposed noise measurement algorithm is sufficiently reliable and accurate for use in the noise assessment applications of CT images.

Considering the growing concerns about the risk of radiation dose in CT examinations, the measurement of noise in patient images will be used more often in daily routine to ensure the balance between image quality and radiation dose is properly maintained based on the ALARA principle (Menzel et al 2000, Yang and Goo 2008, Lee et al 2009). In addition, the ever-evolving CT technology fueled by innovations in detector technologies and sophisticated image reconstruction algorithms is expected to increase the need for a high throughput noise measurements in patient CT images for research purposes as well as for quality assurance tasks in routine practice. Up to now, however, an automated technique for the measurements of CT noises in patient images has been rarely studied, and accordingly most previous studies depended on manual operation for the assessment of image quality in relation to CT technical parameters. Only recently, Christianson et al proposed a technique for the automated measurement of CT noise in which a noise histogram was generated by the standard deviation of ROIs placed within thresholded soft tissue, and the mode value of the noise histogram was taken as the global noise level of a given image (Christianson et al 2015).

Noise measurement in CT images involves the selection of reference tissue and the determination of ROIs. Typically, the standard deviation of CT numbers within an ROI drawn on a homogeneous soft tissue region is taken as a representative image noise. Although seemingly straightforward, the tasks involved in noise measurement require a highly specialized perceptual and coordinated-control ability guiding a series of jobs done in a standardized manner. Of primary importance is discriminating a homogeneous region from a subtle small-scale structure, which is not an easy task and scarcely studied previously. The lack of such discrimination ability and standardized criteria to classify them could lead to the inclusion of small-scale anatomical structures in ROIs, which in turn could result in an overestimation of the image noise. Indeed, the noise levels measured by the radiologists in our study were overestimated across different study groups as compared to the noise measurements by the proposed automated method.

A recent study also reported that a simple computerized noise measurement technique that did not take into account the small-scale anatomic structures produced similar overestimated noise levels in comparison with the reference noise levels that were established by subtracting a pair of images scanned twice in the same conditions (Christianson et al 2015). These reflects the difficulty of discriminating small-scale structures in determining homogeneous ROIs both by human experts and computerized techniques.

Our study employed a novel structure coherence feature in order to effectively discriminate small-scale anatomic structures. We considered the nature of a homogeneous region as having a smaller edginess as well as randomness of pixel orientation. In less noisy images, considering the edginess only might be sufficient to discriminate homogeneous ROIs from the background structures. However, when the strength of the background noise outweighs that of small-scale structures, which might often be the case in low-dose CT scans, the distinction of the edginess between the noise and small-scale structures disappears, thus making the discrimination of a homogeneous region from small-scale structures difficult. In contrast, our composite structure coherence feature combined the randomness of pixel orientation along with the edginess to make the feature more robust even in noisier images. In fact, our feature worked effectively over a wide range of image noise levels: from 7.16 HU in the chest routine study of pediatric patients to 21 HU in the 50% simulated reduced-dose chest study of adult patients. The reliable and accurate performance of our noise measurement technique shown in this study might be attributed mostly to the robustness of the composite structure coherence feature, which was proposed for the first time in this study.

This study placed ROIs with an approximately 1 cm² area on homogeneous fat tissue to measure the CT noise. A larger ROI size would provide more statistically reliable noise measurements at the cost of difficulty in finding the homogeneous region to fit a larger ROI. On the other hand, smaller ROIs, although finding more easily a homogeneous region to fit, could suffer statistical instability in presenting the overall image noise. We followed the AAPM report 39 recommendations and used an ROI size of about 1 cm² area in the measurement of CT noise (AAPM TG-2 1993). We found the ROI size of 1 cm² area was a trade-off for finding homogeneous locations and reliable noise measurements. Meanwhile, 5 ROIs were successfully placed at homogeneous locations in most of the test cases, and we found a slight variation existed among the noise measurements of the 5 ROIs. Therefore, we added a procedure for averaging the noise measurements from the 5 ROIs to improve the reliability of the noise measurements.

The relationship between radiation dose and image quality in different patient groups and body size remains complex and unclear. A previous study reported that the body characteristics of patients vary depending on gender, age, race, and habitat, which were responsible for the complex relationship between radiation dose and image quality, and made the CT scan optimization remain a difficult task even with efforts in clinical practice (Jung and Goo 2008). Therefore, the use of the proposed algorithm in a combination of software tools providing the size-specific dose estimates recently released by AAPM TG-204 (2011) and AAPM TG-220 (2014) allowed an improved understanding of the relationship between various patient factors, CT parameters, patient-specific dose, and noise levels, which in turn would lead to an advancement towards truly individualized optimal CT scanning (Schuhbaeck et al 2013).

This study still has several limitations. First, the image noise was measured only on fat tissue. Although previous studies measured noise levels in soft tissue regions, we chose to use fat as the reference tissue due to the fact that fat is easily found in diverse body parts, and therefore can be useful in assessing noise profiles along the longitudinal body axis. However, there can be a difference in noise levels between fat and soft tissue due to the attenuation difference. Therefore, the noise levels measured in this study cannot be directly applied to the noise assessment of soft tissue. Nonetheless, it should be noted that the proposed noise measurement algorithm is not limited to fat tissue. It can be applied to other different tissue types as needed. An investigation of the relationship of the noise levels between fat and soft tissues in different body sizes and under contrast enhancement would be an interesting research subject.

Second, this study considered only the average global noise level on a CT image. While the use of the average global noise level has been regarded as the primary factor determining the CT image quality and adopted frequently in many studies, other image quality metrics such as CNR, SNR, and NPS need to be assessed for an integrative image quality assessment. In addition, the spatially varying and non-stationary nature of CT noise also needs to be considered in studies investigating the full characteristics of CT noise.

Third, only 2 radiologists were available as expert raters for establishing the reference noise level. As shown in this study, human raters inherently exhibit within and between-rater variability in noise measurements, and thus recruiting more expert raters could have enabled us to establish the reference noise level with greater reliability. Nonetheless, we found that human experts tend to ignore subtle small-scale structures in placing ROIs, which unavoidably leads to an overestimation of the noise level. Therefore, we believe our study results were not influenced significantly by the small number of expert radiologists participating in this study.

This study presented an algorithm for the automated measurements of noise in patient CT images with a novel structure coherence feature. The newly devised structure coherence feature was able to discriminate small-scale structures from homogeneous tissue and enabled us to place ROIs in homogeneous regions with a very high success rate. The noise measurements using the proposed algorithm agreed excellently with the reference noise level established by 2 radiologists as well as the theoretical noise level in the simulated reduced-dose images. The proposed algorithm appears to be sufficiently reliable and accurate for CT noise assessment in patient images, and thus offers the potential for the high throughput assessment of image quality in studies examining the appropriateness of radiation dose and the optimization of CT protocols.

This research was in part supported by a grant of the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health & Welfare, Republic of Korea (grant number: HI14C3287).

This work was in part supported by the Technology Innovation Program (10051357, Development of intelligent low-dose mobile C-arm CT system for intervention) funded By the Ministry of Trade, industry & Energy (MI, Korea).