A comprehensive study on the relationship between the image quality and imaging dose in low-dose cone beam CT

A kV on-board imaging (OBI) system integrated in a TrueBeam™ medical linear accelerator (Varian Medical System, Palo Alto, CA) was used in the experiment. The x-ray tube has a small focal spot of 0.4 mm and a 2.7 mm inherent filtration on the exit window. The imaging detector has 768 × 1024 pixels and the pixel pitch in each dimension is 0.392 mm, which yields an active detector area of 30.1 × 40.1 cm². An anti-scatter grid is mounted on the detector. The distances from the source to the rotation center and to the detector plane are 100 and 150 cm, respectively. A CatPhan® 600 phantom (The Phantom Laboratory, Inc., Salem, NY) was scanned in a full-fan mode with a full-fan bow-tie filter on site (figure 1(a)). In each scan, 364 projections over 200° were acquired.

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The tube voltage was fixed to 100 kVp in all scans. The CatPhan® 600 phantom was scanned under 13 dose levels, i.e. 73.2, 95.6, 109.8, 146.4, 161.04, 190.32, 219.6, 292.8, 329.4, 395.3, 439.2, 585.6 and 878.4 total mAs, corresponding to 0.2, 0.26, 0.3, 0.4, 0.44, 0.52, 0.6, 0.8, 0.9, 1.08, 1.2, 1.6 and 2.4 mAs/view. For each dose level, 46, 61, 91, 121, 182 and 364 projections were extracted with equal angular intervals from the total 364 projections, so that the final experimental database consists of 13 × 6 data points on the DQM, including four groups of data points of equal dose values around 36.4, 72.6, 109.2 and 146.4 total mAs (figure 1(b)).

Although a large database was collected, the measured data is still not dense enough to cover the whole DQM over the clinically relevant range. The main reason is because the minimum angle between two neighboring projections in the OBI system is fixed to 200/360 ⋅ 2π/364 (full-fan mode), and consequently one cannot obtain evenly distributed projections with total projection numbers between 182 and 364 (figure 1(b)). To have a complete view of DQM, we perform a measurement-based simulation as a supplement to the experiment.

A digital phantom (figure 1(c)) was specifically designed for this simulation according to the contrast module of the CatPhan® 600 phantom. The forward x-ray projections were calculated using an analytical approach based on Tang et al (2006). To be more realistic, a non-uniform fluence map caused by the bow-tie filter was measured and used in this simulation. The simulated scanning configuration was exactly the same as that in the experiment. A 12×12 data grid was generated (figure 1(d)). The projection number varies from 30 to 360 at an interval of 30. To simulate different mAs levels, we superimposed noises based on the measured data. The noise model employed here was proposed by Li et al (2004) based on the experimental data and has been further validated in Wang et al (2008). Specifically, the standard deviation of a pixel value can be described by the following formula:

$$\begin{equation} {\rm std}(g_i ) = b_i \exp \left( {\frac{{\mu (g_i )}}{T}} \right), \end{equation} \tag{ 1 }$$

where µ represents the mean, g_i is the detected signal at the pixel i, T is a machine-dependent constant and b_i is determined by the mAs/view and the fluence map. In commissioning the noise model against our experiment, the axis-invariant sinogram data scanned with 2.4 mAs/view were averaged to estimate µ(g_i). One can obtain the variance for each data point at different mAs levels, and then T and b_i can be obtained according to the steps in (Li et al 2004).

To reveal the contrast details and catch the artifacts that may otherwise be invisible in a wide window, we observed the reconstructed images containing low-contrast objects (figures 1(c) and 2(a)–(c)) with a consistent narrow grayscale window of [0.018, 0.025] mm⁻¹, which corresponds to a soft-tissue display window of 375 HU width. The difference between each image and its reference image was also visually investigated with a grayscale window of [−0.00125, 0.00125] mm⁻¹. We used a wide grayscale window of [0.008, 0.032] mm⁻¹ for the image containing high-contrast air and Teflon robs with 3 mm diameter (figure 2(d)). For the resolution slice (figure 2(e)) and the region of interest (ROI) therein (figure 2(f)), [0.008, 0.045] and [0.03, 0.05] mm⁻¹ were used, respectively.

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To generate quantitative IQA scores, we used a number of IQA metrics, including a classic difference-based metric, i.e. relative root mean square error (rRMSE), and a recently proposed perception-based metric, i.e. feature similarity index (FSIM). For the experimental data, the contrast-to-noise ratio (CNR) was also used to further investigate the visibility of the ROIs shown in figure 2(b).

rRMSE.

The conventional rRMSE is defined as

$$\begin{equation} {\rm rRMSE}_1 = \sqrt {\frac{{\sum _{i,j} \big| {f_{i,j} - f_{i,j}^{{\rm ref}} } \big|^2 }}{{\sum _{i,j} \big| {f_{i,j}^{{\rm ref}} } \big|^2 }}} , \end{equation} \tag{ 2 }$$

where f and f^ref represent the evaluation and reference image, respectively, and i, j labels the pixel coordinates in the 2D images. To focus more on the low-contrast objects, we define a second rRMSE as

$$\begin{equation} {\rm rRMSE}_2 = \sqrt {\sum\nolimits_{i,j} {\left( {\frac{{\big| {f_{i,j} - f_{i,j}^{{\rm ref}} } \big|}}{{w_{i,j} }}} \right)^2 } } , \end{equation} \tag{ 3 }$$

with

$$\begin{equation} w_{i,j} = \exp \left( {\left| {\frac{{f_{i,j}^{{\rm ref}} - \mu _{{\rm water}} }}{{\mu _{{\rm water}} - \mu _{{\rm polystyrene}} }}} \right|} \right). \end{equation} \tag{ 4 }$$

Compared with rRMSE₁, rRMSE₂ is more sensitive to the bias introduced by low-contrast objects with attenuation coefficients around µ_water. In this work, µ_water and µ_polystyrene were set to 0.0206 and 0.0196 mm⁻¹, respectively.

FSIM.

It has been recognized that IQA could be more consistent with the human subjective evaluation if the metrics are designed by considering the mechanism of the human visual system. Perception-based metrics were proposed for this purpose. The basic idea is to perform IQA on the structure level rather than the pixel level, mimicking how the human visual system works. A novel metric called FSIM was recently proposed (Zhang et al 2011), where the main features are the phase congruency (PC) of the local structure and the image gradient magnitude (GM). Extensive experiments on six benchmark IQA databases demonstrated that FSIM could achieve higher consistency with the subjective evaluation than other state-of-the-art IQA metrics (Zhang et al 2011). We therefore have used FSIM as an IQA metric in this work. FSIM is defined as

$$\begin{equation} {\rm FSIM} = \frac{{\sum _{i,j} \{ S_{{\rm PC}} \cdot S_{{\rm GM}} \cdot {\rm PC}_m \} }}{{\sum _{i,j} \{ {\rm PC}_m \} }}, \end{equation} \tag{ 5 }$$

by using both PC-based similarity metrics S_PC:

$$\begin{equation} S_{{\rm PC}} = \frac{{{\rm PC}\big( {f_{i,j}^{{\rm ref}} } \big) \cdot {\rm PC}( {f_{i,j} } ) + T_1 }}{{\big[ {{\rm PC}\big( {f_{i,j}^{{\rm ref}} } \big)} \big]^2 + [ {{\rm PC}( {f_{i,j} } )} ]^2 + T_1 }}, \end{equation} \tag{ 6 }$$

and GM-based similarity metrics S_GM:

$$\begin{equation} S_{{\rm GM}} = \frac{{{\rm GM}\big( {f_{i,j}^{{\rm ref}} } \big) \cdot {\rm GM}( {f_{i,j} } ) + T_2 }}{{\big[ {{\rm GM}\big( {f_{i,j}^{{\rm ref}} } \big)} \big]^2 + [ {{\rm GM}( {f_{i,j} } )} ]^2 + T_2 }}, \end{equation} \tag{ 7 }$$

with a PC-based weighting factor PC_m:

$$\begin{equation} {\rm PC}_m = \max \big[ {{\rm PC}\big( {f_{i,j}^{{\rm ref}} } \big),\;{\rm PC}( {f_{i,j} } )} \big]. \end{equation} \tag{ 8 }$$

In (6) and (7), T₁ and T₂ are positive constants to increase the calculation stability. More detailed descriptions of PC and GM are given in Zhang et al (2011). We directly used the code¹ provided by the authors in our evaluation. The FSIM score varies between 0 and 1 with 1 representing the best image quality.

CNR.

The CNR was used for the ROI visibility evaluation for the experimental data. As seen in the contrast slice (figure 2(b)), seven areas within the inner circle were selected as the ROI targets and the corresponding concentric rings were used as backgrounds. The CNR is defined as

$$\begin{equation} {\rm CNR} = \frac{{\big| {\mu \big( {f_{{\rm ROI}}^t } \big) - \mu \big( {f_{{\rm ROI}}^b } \big)} \big|}}{{{\rm std}\big( {f_{{\rm ROI}}^t } \big) + {\rm std}\big( {f_{{\rm ROI}}^b } \big)}}, \end{equation} \tag{ 9 }$$

where the superscripts t and b represent the target and background, respectively.

DQMs were generated based on the simulated data (figure 1(c)) and measured data (figures 2(a) and (c)). Compared with the subjective visual inspection methods for tuning β as in many other works, in this work we combine a subjective inspection method with objective metrics to take advantage of each method's strengths. Human visual inspection is commonly considered as the gold standard for image quality assessment. Currently, no IQA metric performs equally as the human visual system. Each metric is more or less biased by emphasizing certain aspects of the image quality. However, it is hard to determine the best image from several very similar candidates with visual inspection. In that case, objective metrics can be used to help identify the best image with a quantitative score.

The detailed steps are as follows.

• (1)  
  A reference image was reconstructed as the gold standard for evaluation. For the simulation data, the reference image was reconstructed from 1080 noise-free projections, while for the experimental data, the reference image was reconstructed from 364 projections scanned at the highest imaging dose (2.4 mAs/view and 873.6 total mAs).
• (2)  
  Three β values with similarly good visual performance were selected manually as candidates.
• (3)  
  IQA metrics were then used to determine the optimal β value. If for a data point different optimal β values were indicated by different metrics, they were averaged to obtain the final optimal β value.
• (4)  
  The DQM was generated by interpolating the image quality scores of all data points as shown in figures 1(b) and (d). Note that due to the accuracy consideration, for the experimental data, only the dense data points inside the red box in figure 1(b) were used.

Further analysis was performed for data points on the iso-dose lines in DQMs. For the images containing low-contrast targets (figures 2(a) and (c)), we closely inspected them using visual inspection and rRMSE, FSIM and CNR. We also inspected the resolution slice (figure 2(f)) and the slices containing high-contrast targets (figures 2(a) and (d)).

Similar to figure 3, the results for the measurement data are shown in figure 4. The DQMs in terms of rRMSE₁, rRMSE₂ and FSIM are shown in figure 4(a), with data points representing four iso-dose levels around 36.4, 72.8, 109.2 and 145.6 total mAs. Only the dense data points (figure 1(b)) were used for building these DQMs to ensure accuracy. In figure 4(b), the IQA scores of all data points are plotted with logarithmic-scale applied to the horizontal axis. The optimal β values for different data points are shown in figure 4(c).

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Basically, figure 4 verifies figure 3; the observations from figure 4 are consistent with those from figure 3. From figure 4(a), it is clear that the optimal image quality is obtained with a protocol of the medium number of views and the medium mAs/view. As a discrete counterpart of figure 3(e), figure 4(b) also exhibits that image quality degradation is not evident with imaging doses from 576 to 100 total mAs and at a much steeper rate after 40 total mAs. Moreover, the IQA scores vary at the same total mAs value, indicating that the image quality varies even for the same dose level due to the use of different scan protocols. Figure 4(c) illustrates that larger β values are needed for low-dose levels, consistent with figure 3(d).

Corresponding to the four iso-dose levels (36.4, 72.8, 109.2 and 145.6 total mAs), the images with different scan protocols are shown in figures 5–8, in which our focus is on a low-contrast object indicated by the yellow arrow in the reference image (last column, figure 5). A specific protocol is represented by a×b(c), where a represents the number of projections, b is the mAs/view and c is the actual total mAs. Note that some data points are not available due to the experiment limitation on the fixed minimum view interval and discretely collected mAs levels. For example, 364×0.1 is not available for the 36.4 total mAs level (figure 5) because 0.2 mAs is the minimum mAs provided by the machine. For a similar reason, little differences existed within the iso-dose level, e.g. the actual values for the 36.4 total mAs level are between 36.3 and 36.8, which are labeled accordingly in figures 5–8.

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From figure 5, it is clear that severe artifacts exist in the sparse-view image (46×0.8) where the low-contrast object is indistinguishable. The artifacts are much alleviated (yet still visible) in 61×0.6, and the low-contrast object starts emerging. It can be seen that the five reconstructed images can be ranked from high to low quality based on the visibility of the low-contrast object and the difference images in the following order: 91×0.4, 121×0.3, 182×0.2, 61×0.6 and 46×0.8, which is consistent with our observations from figures 3 and 4.

The observations based on the difference images from figures 6–8 are consistent with that from figure 5, i.e. scan protocols with a medium number of projections (∼91–121) and a medium level of mAs/view yield reconstruction images of optimal quality. However, based on the visibility of the low-contrast object, the quality of the images scanned with the number of projections greater than 91 is very similar, which is also consistent with figures 3 and 4. We also noted that it is evident that high-contrast objects degrade dramatically in the image reconstructed from more projections. When the imaging dose level is fixed, using more projections means a lower SNR in each projection. In such cases, image degradation is expected and all objects will be degraded to some extent. However, it is more profound for the high-contrast object likely due to the large intensity difference. Hence, when plotting the difference image at a certain window level, the degradation of high-contrast object is more obvious.

For the images in figures 5–8, the corresponding rRMSE₁, rRMSE₂ and FSIM scores as well as the CNR scores for different ROIs are shown in figures 9 and 10.

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In figure 9, all the global metrics show the same phenomenon as observed from the visual inspection (figures 5–8), i.e. the optimal image quality can be achieved at the middle of each iso-dose line, and this phenomenon is more evident at the lower dose levels such as 36.4 and 72.8 total mAs. We can also see that the image quality has a considerable improvement when the dose is increased from 36.4 to 72.8 total mAs, while less considerable for the total mAs changes from 72.8 to 145.6.

In figure 10, the CNR scores are given for different total dose levels and different ROIs. We also plot the CNR scores at 873.6 total mAs as a reference. From this figure, we can see that the maximum CNR scores for each ROI locate in the range of 91–180 projections, which again is consistent with the observations from figures 3–9. This phenomenon is more obvious for the two low-contrast ROIs at the 1 and 11 o'clock directions (yellow and red) and at lower dose levels. For the high-contrast ROIs such as Teflon and air at the 5 and 6 o'clock directions (blue and cyan), this phenomenon is not obvious. Furthermore, the CNR only decreases for the low-contrast ROIs (black, yellow and red) and does not change significantly for high-contrast ROIs. Specifically, if we look at the red ROI at the 1 o'clock direction, which is the low-contrast object used for visual detection in figures 5–8, we can find that its CNR changes most significantly with the dose variation.

The reconstructed ROI images in the resolution slice are shown in figure 11. In the reference image, we can discriminate up to 9 line pairs per cm (the bottom-right corner of the image panel). For the 36.4 total mAs level, we can only roughly visualize 8 line pairs. For the 72.8 total mAs level, we can identify 8 line pairs per cm clearly with all the scan protocols, and almost 9 line pairs per cm with protocol of 121×0.6. When the dose is increased to 109.2 and 145.6 total mAs the overall clarity is improved.

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The general trend observed from the high-resolution cases is quite similar to that from the low-contrast cases. It seems that the optimal dose allocation scheme of 72.8 total mAs, i.e. 121×0.6 offers an acceptable resolution compared with the reference (873.6 total mAs). If one needs a more robust and easy discrimination of 9 line pairs per cm, over 100 total mAs are necessary.

The reconstructed images acquired at extremely low-dose levels are shown in figure 12 for different imaging tasks and compared with the reference images acquired at the highest dose level (873.6 total mAs). It clearly shows that neither 12.2 nor 18.2 total mAs is sufficient for the low-contrast or high-resolution objects. However, with even 12.2 total mAs we can still clearly see the high-contrast objects with large enough dimension, e.g., 3 mm diameters for the small Teflon and air rob. This is consistent with the CNR results for the high-contrast objects shown in figure 10, i.e. the visibility of high-contrast ROIs suffers the least from the dose reduction. Therefore, it may be quite feasible to use an extremely low-dose level like 12.2 total mAs for certain IGRT tasks such as bony structure-based patient positioning.

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