Journal of X-Ray Science and Technology 21 (2013) 467–479 DOI 10.3233/XST-130402 IOS Press
467
Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT Min Yanga,∗ , Shengling Duana , Jinghui Duanb , Xiaolong Wanga , Xingdong Lic , Fanyong Mengd,∗ and Jianhai Zhange a School
of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing, China b China Information Security Certification Center, Beijing, China c National Institute of Metrology, Beijing, China d State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing, China e School of Mechanical Engineering, Sungkyunkwan University, Seoul, Korea
Received 22 April 2013 Revised 5 September 2013 Accepted 8 September 2013 Abstract. Fast-continuous-rotation is an effective measure to improve the scanning speed and decrease the radiation dose for cone-beam CT. However, because of acceleration and deceleration of the motor, as well as the response lag of the scanning control terminals to the host PC, uneven-distributed and redundant projections are inevitably created, which seriously decrease the quality of the reconstruction images. In this paper, we first analyzed the aspects of the theoretical sequence chart of the fastcontinuous-rotation mode. Then, an optimized sequence chart was proposed by extending the rotation angle span to ensure the effective 2π-span projections were situated in the stable rotation stage. In order to match the rotation angle with the projection image accurately, structure similarity (SSIM) index was used as a control parameter for extraction of the effective projection sequence which was exactly the complete projection data for image reconstruction. The experimental results showed that SSIM based method had a high accuracy of projection view locating and was easy to realize. Keywords: Cone-beam CT, fast-continuous-rotation scanning, data redundancy, structural similarity
∗ Corresponding authors: Min Yang, School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100191, China. E-mail:
[email protected]; Fanyong Meng, State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China. E-mail:
[email protected].
c 2013 – IOS Press and the authors. All rights reserved 0895-3996/13/$27.50
468
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT
Fig. 1. The principal diagram of a cone-beam CT scanning system. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/XST-130402)
1. Introduction As a kind of advanced nondestructive testing technology, cone-beam CT technology can accurately reconstruct the internal 3D structure of the tested object and quantitatively show its interior physical properties, such as density distribution, defects’ shape and location [1–5]. Figure 1 is the principal diagram of a cone-beam CT scanning system. The cone-beam X-rays penetrate the tested object fixed on the rotary table and reach the flat-panel detector. The flat-panel detector collects DR (Digital Radiography) projections of the tested object at different imaging views among 360 degrees while the tested object is rotating at the drive of the rotary table. With all DR projections, 3D reconstruction is performed and cross-sectional images are obtained. The host PC is responsible for the unified control of the secondary control terminals such as the X-ray source, the rotary motor and the flat-panel detector by an interactive communication means. Step-by-step-rotation and continuous-rotation scanning modes are most commonly applied in conebeam CT system. For the first scanning mode, the motor rotates step by step and the detector collects projections when the object is stationary, which guarantees the accuracy of the stepping angle and avoids motion blur. Furthermore, this scanning mode does not cause redundancy or uneven-distributed projection data due to acceleration and deceleration of the motor, as well as the response lag of the scanning control terminals to the host PC. Thus, the rotation angle and its corresponding projection can accurately match each other, which will be beneficial to obtain reconstructed images with high resolution. In the area of computed tomography, scanning time is equivalent to the number of projections in some sense. In order to reduce the scanning time, one direct method is to reduce the number of projections by increasing the stepping angle or limited-angle scanning, namely the rotation-angle span of the object is lesser than
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT
469
360 degrees [6]. This method usually needs complicated algorithms to get ideal reconstruction images, such as a constrained total variation (TV) minimization algorithm [7], The adaptive steepest-descentprojection-onto-convex-sets (ASD-POCS) algorithm [8]. Another method to reduce the scanning time is the fast-continuous-rotation scanning mode, which is suitable for the situations when faster scanning speed or lower radiation dose are required, such as observing interior dynamic changes of the object to be scanned during the course of loading process or scanning living body for medical application [9,10]. This kind of scanning mode can obtain sufficient projections for image reconstruction within a short period of time. The object rotates continuously while the detector collects projection images at a fixed acquisition frame frequency, which needs high stability of the rotating motion and high synchronicity of the communication responses between the control terminals and the host PC. The rotation step angle needed in the reconstruction algorithm is determined by the motor’s rotation speed and detector’s acquisition frame frequency. In our application, we used the fast-continuous-rotation scanning mode to observe an object with slowly changing internal structure. The motor made a round within 15 seconds and the acquisition frame frequency of the detector was 50 frames per second. Theoretically in every round there would be 750 frames of projection collected for image reconstruction. However, due to the acceleration and deceleration of the motor on startup and end stages, fluctuation of the rotation speed, as well as response lag of the control terminals to the host PC, uneven-distributed and redundant projections were created, and the number of the total projections was always unstable. So in practical realization it is necessary to remove the unused projections to ensure the complete 2π -span projections are obtained for accurate reconstruction. Accurate location of image data information is crucial in industrial computed tomography (ICT) application. Li [11] proposed a method by using FPIT (finite plane integral transform) and planelet to find out approximate locations of the cracks and then extracted their surface precisely in ICT volume data. Yin [12] presented a parametric boundary estimation approach to estimate orientation and the position of targeted objects. The above algorithms use complex operation steps or iterative computation, time-consuming is their main limitations for engineering application. Kuma [13] proposed an available partition method by calculating the variance between the initial projection (at 0 degree) and its following projections among a certain neighborhood to realize the 2π -position projection locating. The position where the variance reaches its minimum value indicates the position of 2π angle. In this paper, the scanning mode we concerned is that the rotary table rotates continuously with a fast speed and the detector collects images with a high acquisition frame frequency. Meanwhile, when the detector captures DR projections with a high acquisition frame frequency, images with high-level noise will be produced due to short exposure time and quantum noise from the X-ray source. In this case, we found that U. Kuma’s method was likely to bring unstable results because it is sensitive to image noise. In this paper, we first analyzed the theoretical sequence chart of the fast-continuous-rotation scanning mode, then, optimized the sequence chart to ensure the effective 2π -span projections lied in the stable rotation stage in Section 2. In Section 3, a method based on SSIM for extra projection identification is proposed. SSIM index is based on the theory of structural similarity. It defines structure information independent of brightness and contrast, and reflects the attributes of the objects more objectively. SSIM is widely used in the similarity comparison between two images with simple operation and high accuracy [14]. In Section 4, some experimental results are presented to verify the effectiveness of the identification method. Finally, the conclusion is drawn in the last section. 2. Scanning sequence chart optimization The theoretical sequence chart of the fast-continuous-rotation scanning mode discussed here is shown in Fig. 2. When the scanning control task begins, the host PC sends commands to the motion controller
470
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT
Fig. 2. Theoretical sequence chart of the fast-continuous-rotation scanning mode.
Fig. 3. Optimized sequence chart of the fast-continuous-rotation scanning mode.
of the rotary table and drives the motor to rotate. During the startup stage of the motor, its rotation speed is accelerated from zero to a stable angular velocity ω . As soon as the rotation speed reaches a stable value ω , the host PC sends commands to the detector and triggers it to collect projections with a fixed acquisition frame frequency. All the collected projection data will be automatically transferred to the RAM or hard disk of the host PC through data acquisition and transmission module of the detector. When the rotation angle reaches 2π , it is time for the host PC to terminate the scanning process. The host PC sends commands to the motor and the detector to stop rotation and data collection, respectively. Due to the deceleration of the motor on the end stages, some uneven-distributed projections are created, in particular for high acquisition frame frequency mode, the number of the uneven-distributed projections can’t be neglected. Also, it takes a certain time for the detector to respond to the commands of ending data collection from the host PC. Thus, during the short lag time some redundant projections are created and can’t be ignored either. Both the uneven-distributed and redundant projections do not contribute to the
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT
471
image reconstruction. Consequently, after one cycle of scanning is finished, if the collected projections are assumed to be even-distributed among 2π -rotation-angle span and used for image reconstruction directly, artifacts and shape distortion will emerge in the reconstruction images. For example, when the acquisition frame frequency of the detector is 50 frames per second, and the lag time is 0.5 s, there will be about 25 extra projections with unknown corresponding rotation angle. From Fig. 2 we can see that the extra projections, namely the uneven-distributed and redundant projections, lie in the deceleration and rest stages of the rotary table. Obviously they must be removed before image reconstruction. Here we optimized the scanning sequence chart as shown in Fig. 3 and realized it by the following steps. Step 1: When a scanning cycle starts, the host PC sends commands to the motion controller of the rotary table and drives the motor to rotate. During the startup stage of the motor, its rotation speed is accelerated from zero to a stable angular velocity ω . Generally the value of ω is 5◦ /s ∼ 30◦ /s. Step 2: As soon as the rotation speed reaches a stable value ω , the host PC sends commands to the detector and triggers it to collect projections with a fixed acquisition frame frequency. The acquisition frame frequency is an indicator parameter to describe the projection numbers collected by the detector per second. For fast-continuous-rotation scanning mode, the detector’s acquisition frame frequency is 50 ∼ 100 frames/s. Step 3: During the rotation, the host PC records the rotation angle and when the total rotation angle span reaches 360◦ + θ , the host PC sends commands to the motor and detector to stop rotation and data collection, respectively. θ is an extra angle to ensure the uneven-distributed and redundant projection data lie in θ -rotation span. By this way, although there are still extra projections in the collected projection sequence, the effective 2π -span projections are situated in the stable rotation stage. 3. Extra projection data identification method After one scanning cycle is finished, a projection sequence with extra data is acquired, here we define the original projection sequence as P1 {P (x, y)1 , P (x, y)2 , . . . P (x, y)i . . . , P (x, y)N }. Where, x and y are the pixel coordinates of the projection image, P (x, y)i represents the ith projection, and N is the total projection number. Before identifying the extra data in the projection sequence, pre-processing is a necessary step to ensure the identification accuracy. Here two important methods are employed. Logarithmic transformation, X-Ray attenuation obeys exponential function, namely Beer’s rule. For CT reconstruction, the projection value (also beam-sum) is a linear function of the X-rays’ penetrating distance in the object. So we must transform the original projection image to satisfy the linear relationship by logarithmic transformation. P (x, y)log i = ln
max(P (x, y)i ) , P (x, y)i
(1)
where, max(P (x, y)i ) is the maximum value of the projection P (x, y)i . Noise reduction, When the detector captures DR projections with a high acquisition frame frequency, images with high-level noise will be produced due to short exposure time and quantum noise from the X-ray source. Here we used NL-means (Non-local means) algorithm to realize the reduction of image noise [15–17]. This algorithm originates from the neighborhood filtering algorithm and is a promotion of this algorithm. Instead of using single-pixel comparison, this method uses the adjacent pixels’ gray-level distribution to execute the comparison. The weighted coefficients are decided in line with the similarity
472
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT
among the adjacent pixels. The original NL-means method easily brings out “staircasing” artifacts in the flat region of the image. Thus, we added gradient information to the weighted coefficient calculation with the aim of weakening “staircasing” artifacts. The improved 2D NL-means algorithm is [18] v N L (i) = w(i, j)v(j), (2) j∈I 2
i )−∇v(Nj ))2,a 1 − (v(Ni )−v(Nj ))(∇v(N h2 e , Z(i) (v(Ni )−v(Nj ))(∇v(Ni )−∇v(Nj ))22,a h2 Z(i) = e− ,
w(i, j) =
(3) (4)
j
where, vN L is the denoised image and v is the noisy image, i is the image pixel number, I is the set of all image pixels, ∇v is the gradient operator, which actually can be calculated by Sobel operator with a noise suppression effect. v(Ni ) and v(Nj ) are vectors which denote a square neighborhood with a fixed size and centered at pixel i and j . (v(Ni ) − v(Mj ))(∇v(Ni ) − ∇v(Nj ))22,a is a function of weighted Euclidean distance, a(> 0) is the standard deviation of the Gaussian kernel. h is decided by the standard deviation of the image noise. By adding the gradient information in the algorithm, the neighborhood correlation among the image pixels decreases, which does not only makes the flat area smoother but also keeps the details clearer, thus artifacts caused by the original NL-means algorithm are removed effectively. Here we define the denoised projection sequence as P2 {P (x, y)denoise , P (x, y)denoise , . . . P (x, y)denoise . . . , P (x, y)denoise }. 1 2 i N
According the detector’s acquisition frame frequency and the rotation speed of the rotary table, we can estimate the theoretical projection number at 2π position among the whole rotation angle span. The , obviously M < N . After theoretical corresponding projection at 2π position is named as P (x, y)denoise M P (x, y)denoise is located, the third projection sequence as shown in Fig. 3 is constructed M denoise denoise P3 {P (x, y)denoise . . . , P (x, y)denoise }, M −Δ , P (x, y)M −Δ+1 , . . . P (x, y)M N
where, the suggested value of Δ is 20 ∼ 50. Then we calculate each SSIM (structure similarity) index between the first projection P (x, y)denoise and each projection in the third projection sequence P3 . The 1 calculation formula of SSIM is [14] (2μAμB)(2σAB + C2) SSIM(A,B) = , (5) (μA + μB + C1)(σA + σB + C2) where, A is the projection P (x, y)denoise and B is an arbitrary projection in P3 . μA and μB are the 1 mean value of A and B. σA and σB are the standard deviation of A and B. σAB is the covariance between A and B. C1 and C2 are constants used to ensure the denominator is nonzero. The values of C1 and C2 are proved to be non-sensitive to the SSIM results and can be set in a wide range with small values. Here we set C1 = C2 = 0.02. The lager SSIM indicates the more similarity between the image couple. When SSIM coefficient reaches the maximum value, the corresponding projection defined as P (x, y)denoise in P3 is the one at 2π position during the rotation cycle. Q indicates the number of Q projection P (x, y)denoise . Obviously, due to the fluctuation of the rotation speed and the response lag of Q the control terminals to the host PC, the relationship between Q and M is uncertain, namely Q > M , Q = M and Q < M are all possible. Once P (x, y)denoise is accurately located, the extra projections Q can be removed and the effective projection sequence is finally achieved Pef f ective {P (x, y)denoise , P (x, y)denoise , . . . P (x, y)denoise . . . , P (x, y)denoise }. 1 2 i Q
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT
473
Fig. 4. A Cone-beam CT scanning system. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/ XST-130402)
4. Experimental results and analysis In our experiment, the optimized sequence chart and the extra projections identification method are adopted on a cone-beam CT scanning system as show in Fig. 4. The basic scanning parameters are Acquisition frame frequency: 50 frame/s, Rotation speed: 24 degrees/s, Pixel size: 200 μm, Projection size: 512 × 512. We first checked the scanning sequence chart shown in Fig. 2. Theoretically we can obtain 750 projections if there were no any response lag and desynchrony. But actually 778 projections were collected within a scanning cycle. In order to present a clearer comparison, we extracted the central row of each projection and integrated them to a new image which was generally called central sinogram. The central row is the row data passing the projection point of the X-ray focus on each projection image. For the central slice reconstruction, the cone-beam CT algorithm is the same as 2D fan-beam CT algorithm [19– 21]. Therefore, we used central sinogram to reconstruct the central slice by fan-beam CT algorithm. Figure 5(a) is the denoised central sinogram, from which we can see obvious extra data including undistributed and redundant projections. Some of these data were collected when the tested object was in the rest state, so the row data close to the bottom of the central sinogram were almost same, which constructed a vertical bar pattern. Figure 5(b) is a comparison of the profiles from the same row of noisy sinogram and denoised sinogram, from which we can find that the image noise are reduced effectively by NL-means method. When we applied the central sinogram to image reconstruction directly, a distorted image was produced as shown in Fig. 5(c). We then repeated another scanning cycle through the optimized sequence chart as shown in Fig. 3. The rotation speed and the acquisition frame frequency were not changed except that the total rotation
474
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT
(a) Central sinogram
(b) Profiles from the same row of noisy and denoised sinograms
(c) Central slice with distortion
Fig. 5. The central sinogram and slice under the theoretical sequence chart.
angle was 384◦, which ensured the effective 2π -span projections were situated in the stable rotation stage. Theoretically 800 projections would be acquired, but actually 826 projections were finally collected, which constructed the original projection sequence P1 . The central sinogram extracted from P1 also included extra projection data, but its height was larger than the height of Fig. 5(a). After the logarithmic transformation and noise reduction, the denoised projection sequence P2 was obtained. According to the rotation speed and acquisition frame frequency, we knew that the theoretical projection number at 360◦ was 750. In theory, the first projection at 0◦ (P (x, y)denoise ) is the same as No. 750 1 denoise denoise (P (x, y)750 ) projection. Thus, if the first projection P (x, y)1 subtracts P (x, y)denoise , the result 750 should be a zero-value image. The subtracting result shown in Fig. 6(a) is a image with obvious leftover artifacts for the real experimental data, which hints that the real 2π -position projection deviates from its theoretical position. In line with the above-described method, the third projection sequence including projections from P (x, y)denoise to P (x, y)denoise , namely P3 was constructed. Then SSIMs between 720 826 denoise P (x, y)1 and each projection in P3 were calculated and plotted in Fig. 6(d). The maximum value of SSIM is 0.9920 and its corresponding projection number is 763, namely P (x, y)denoise is the accurate 763 . When projection P (x, y)denoise sub2π -position projection and is nearly the same as P (x, y)denoise 1 1
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT
denoise
(a) P(x,y) 1
denoise
denoise
P(x,y) 750
(b) P(x,y) 1
(c) A comparison of the profiles from the same row of Fig. 6(a) and Fig. 6(b)
denoise
P(x,y) 763
(d) Distribution of SSIM
Fig. 6. The calculation results of SSIM.
(a) The effective central sinogram
(b) The corrected central slice
Fig. 7. The central sinogram and slice under the proposed identification method.
475
476
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT 350
0.9918 300
0.9916
Standard deviations
250
SSIM
0.9914
0.9912
0.991
150
100
0.9908
50
0.9906 720
200
730
740
750
760
770
780
790
800
810
820
0 720
730
740
750
760
770
780
790
800
810
820
Projection view number
Projection view number
(a) Distribution of the SSIMs
(c) Central slice under SSIM based method
(b) Distribution of the standard deviation
(d) Central slice under the minimum standard deviation based method
Fig. 8. Comparison of different identification methods.
tracts P (x, y)denoise , the result is a noise image with small values and almost invisible leftover artifacts, 763 as shown in Fig. 6(b). Figure 6(c) is a comparison of the profiles from the same row of Fig. 6(a) and (b), which clearly demonstrates that the SSIM based 2π -position projection is much closer to P (x, y)denoise . 1 After the 2π -position projection was accurately located, the extra data were removed and the effective projection sequence Peffective was achieved. Figure 7(a) is the central sinogram from Peffective , from which we can find that the extra data are well removed. Using the effective sinogram for reconstruction, a better result without distortion and artifacts is obtained as shown in Fig. 7(b). We also compared the SSIM based method with the minimum standard deviation based method proposed by Kuma. Because Kuma’s method is used for 2D CT application cases, we extracted the central sinogram of a resolution bar and calculated 2π -position projection number by the two different methods. Here we define the central sinogram as S(i, j). According to Kuma’s method, the variances between the initial projection (at 0◦ ) and its following projections among a certain neighborhood were calculated and sorted. The position where the variance reached its minimum value indicated the location of the 2π -position projection. Namely, S dif f (i, j) = S(i, 1) − S(i, j), Ns j Np
std(j) =
S0 dif f (S (i, j) − MeanVal (S dif f (i, j))2 i=1 S0 − 1
N 2π = j|std(j) = min(std(j))
,
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT
477
Table 1 Location results of 2π-position projection at different rotation speeds Rotation speed (degrees/s) Total frames Theoretical 2π-position projection number SSIM Accurate 2π-position projection number PSNR
24 826 750 0.9920 763 −
20 977 900 0.9922 907 17.230
16 1217 1125 0.9929 1133 19.775
12 1612 1500 0.9933 1509 24.018
where, Ns is the starting position of the reference neighborhood and Np is the total number of the original projections. S0 is the width of the sinogram, MeanVal is the mean value calculating operator. N 2π is the 2π -position projection number. Figure 8(a) and (b) are the calculation results of SSIM and standard deviation. The projection number at the maximum value of SSIM is 761, while at the minimum standard deviation value, the projection number is 752. When we used the two effective sinograms with different height figured out by the two methods to reconstruct the central slice image, different results were achieved as shown in Fig. 8(c) and (d), from which we can find that by Kuma’s method, one side of the 1.5 Lp/mm pattern is blur and image distortion exits. In addition, we also validated the proposed method under different rotation speed when the acquisition frame frequency was fixed at 50 frames/s. The results are shown in Table 1. When we used the effective sinograms to reconstruct the central slice at different rotation speeds, we found that all the slices were free of distortion, which proved that the proposed method had a good accuracy and repeatability. On further analysis, we calculated Peak Signal to Noise Ratios (PSNRs) of each slice. The slice at 24◦/s was used as the reference image to calculate PSNR. PSNR is used to measure the noise reduction effect and its larger value indicates the smoother processed image [22–24]. We found that as the rotation speed decreased, the PSNR of the slice increased. The reason is that when the rotation speed became lower at a fixed acquisition frame frequency, more scanning time was needed, which resulted in that more projections were collected. Therefore, more effective projections contributed to the back projection and the final reconstructed slices became smoother with higher PSNR. 5. Conclusions Fast-continuous-rotation is an effective measure to improve the scanning speed and decrease radiation dose for cone-beam CT. However, because of the high rotation speed, high acquisition frame frequency, the acceleration and deceleration of the motor on startup and end stages, the fluctuation of the rotation speed, as well as the response lag of the scanning control terminals to the host PC, uneven-distributed and redundant projections are inevitably created, which seriously decrease the quality of the reconstruction images. In this paper, we first analyzed the aspects of the theoretical sequence chart of the fast-continuous-rotation scanning mode, then, optimized the sequence chart by extending the rotation angle span to ensure the effective 2π -span projections were situated in the stable rotation stage. In order to match the rotation angle with the projection image accurately, structure similarity (SSIM) index was used as a control parameter to extract effective projection sequence, which was exactly the complete projection data for image reconstruction. SSIM is a parameter to describe the similarity between two images. The lager SSIM indicates the more similarity between the image couple. Thus, the position where SSIM reaches the maximum value is the one where 2π -position projection lies. This identification method can be embedded in the pre-processing module of a cone-beam CT scanning system. During the pre-processing, this method can automatically identify the uneven-distributed and redundant projections
478
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT
and remove them, so as to ensure the reconstruction accuracy. The experimental results show that SSIM based method has a high accuracy of projection view locating and is easy to realize. Acknowledgments This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grants 11275019, 21106158 and 61077011, in part by the National State Key Laboratory of Multiphase Complex Systems under Grant MPCS-2011-D-03, in part by the National Key Technology R&D Program of China under Grant 2011BAI02B02, and in part by the National Key Scientific Apparatus Development of Special Item of China under grant 2013YQ240803. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
E.L. Ritman, Micro-computed tomography – current status and developments, Annual Review of Biomedical Engineering 6 (2004), 185–208. S.C. Lee, H.K. Kim, I.K. Chun et al., A flat-panel detector based micro-CT system: performance evaluation for smallanimal imaging, Physics in Medicine and Biology 48 (2003), 4173–4185. M. Altunbas, C. Shaw and L. Chen, Reduction of ring artifacts in cone beam CT: artifact detection and correction for Flat Panel Imagers, Medical Physics 33 (2006), 2287–2295. E.Y. Sidky and X. Pan, Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization, Physics in Medicine and Biology 53 (2008), 4777–4807. G.H. Chen, J. Tang and S. Leng, Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly under sampled data sets, Medical Physics 35 (2008), 660–663. Y. Lu, Z. Yang, J. Zhao and G. Wang, TV-based image reconstruction of multiple objects in a fixed source-detector geometry, Journal of X-Ray Science and Technology 20 (2012), 277–289. E.Y. Sidky, K.M. Kao and X. Pan, Accurate image reconstruction from few-views and limited-angle data in divergentbeam CT, Journal of X-Ray Science and Technology 14 (2006), 119–139. X. han, J. Bian, E.L. Ritman, E. Sidky and X. Pan, Optimization-based reconstruction of sparse images from few-view projections, Physics in Medicine and Biology 57 (2012), 5245–5273. V.V. Nagarkar, J.S. Gordon, S. Vasile et al., High resolution X-Ray sensor for non-destructive evaluation, IEEE Transactions on Nuclear Science 43 (1996), 1559–1563. X. Han, J. Bian, D.R. Eaker, T.L. Kline, E.Y. Sidky, E.L. Ritman and X. Pan, Algorithm-enabled low-dose micro-CT imaging, IEEE Transactions on Medical Imaging 30 (2011), 606–620. Z. Li, L. Zeng, X. Zou and C. Xiang, Crack surface extraction of industrial CT volume data using FPIT and planelet, Journal of X-Ray Science and Technology 19 (2011), 1–12. Z. Yin, K. Khare and B.D. Man, Parametric boundary reconstruction algorithm for industrial CT metrology application, Journal of X-Ray Science and Technology 17 (2009), 115–133. U. Kumar, G.S. Ramakrishna, A.S. Pendharkar and S. Kailas, A statistical correction method for inimization of systemic artefact in a continuous-rotate X-ray based industrial CT system, Nuclear Instruments and Methods in Physics Research Section A 515 (2003), 829–839. Z. Wang, A.C. Bovik, H.R. Sheikh and E.P. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Transactions on Image Processing 13 (2004), 600–612. A. Buades, B. Coll and J.M. Morel, A non-local algorithm for image denoising, IEEE International Conference on Computer Vision and Pattern Recognition, Spain (2005), 60–65. B.L. Li, M. Yang and J.J. Li, Denoising of micro-CT image based on improved NL-means algorithm, Journal of Beihang University of Aeronautics and Astronautics 35 (2009), 833–837 (in Chinese). M. Yang, J. Zhang, S. Jin et al., Imaging and measuring methods for coating layer thickness of TRISO-coated fuel particles with high accuracy, NDT&E International 55 (2013), 82–89. M. Yang, Y. Yang and C. Wang, A New 3D Information acquisition method of micro-drilling marks on ancient perforated stone bead through micro-CT, Journal of X-Ray Science and Technology 19(2011), 333–343. L.A. Feldcamp, L.C. Davis and J.W. Kress, Practical cone-beam algorithm, J Opt Soc Am Al (1984), 612–619. M. Yang, J.X. Jin and B. Li, A new method to determine the projected coordinate origin of cone-beam CT system using elliptical projection, Chinese Physics C (HEP & NP) 34 (2010), 1665–1670.
M. Yang et al. / Extra projection data identification method for fast-continuous-rotation industrial cone-beam CT [21] [22] [23] [24]
479
M. Yang, H. Gao, X. Li et al., A new method to determine the center of rotation shift in 2D-CT scanning system using image cross correlation, NDT&E International 46 (2012), 48–54. Q. Hyunh-Thu and M. Ghanbari, Scope of Validity of PSNR in Image/Video Quality Assessment, Electronics Letters 44 (2008), 800–801. H. Yu, G. Cao, L. Burk, Y. Lee, J. Lu, P. Santago, O. Zhou and G. Wang, Compressive sampling based interior reconstruction for dynamic carbon nanotube micro-CT, Journal of X-Ray Science and Technology 17 (2009), 295–303. X. Yang, Y. Meng, Q. Luo and H. Gong, High resolution in vivo micro-CT with flat panel detector based on amorphous silicon, Journal of X-Ray Science and Technology 18 (2010), 381–392.
