Optimization of multi-axis control for metal artifact reduction in X-ray computed tomography

When computed tomography (CT) is used to inspect electronic devices, strong streaks called metal artifacts are produced in the reconstructed image. One of the factors that induce metal artifacts is beam hardening, which is caused by a stack of metals contained in electronic devices saturating incident X-rays. To avoid saturation of X-ray intensities, we proposed a new CT approach with a multi-axis rotation mechanism in our previous study. In this paper, we investigate the optimization of multiaxis control and propose an effective reconstruction algorithm. The results of our simulation experiments show that metal artifacts could be suppressed by avoiding saturation of transmitted X-ray intensities.


Introduction
Computed tomography (CT) has been widely used as a diagnostic and inspection technique.Although CT has been in widespread use for decades, various imaging artifact problems.In particular, because strong streaks and dark stripes called metal artifacts are produced in images from metal pieces, it is still especially difficult to inspect objects that contain a lot of metals, such as electronic devices, by CT. Figure 1 shows cross-sectional images of electronic devices with metal artifacts.Metal artifacts are caused by complex factors [1], but the two major ones are beam hardening and saturation.It is known that when scanning high-attenuation objects, the low-energy band of the incident X-rays is strongly suppressed; i.e., the spectrum becomes richer in the high-energy band.Furthermore, when there are numerous metal pieces or there are metals with a high atomic number, such as iron, platinum, and lead, the incident X-rays are extremely attenuated, and it becomes impossible to distinguish between the absorption by objects and noise.We call this state X-ray saturation.In each case, discrepancies arise during the back-projection calculation that then generate metal artifacts.Many algorithms for metal artifact reduction have been proposed, but this problem has not sufficiently solved yet.Most conventional studies include remediation of projection data or reconstruction algorithms.W.A. Kalender et al. proposed a method using linear interpolations to metal regions on projection data [2], and E. Meyer et al. proposed normalized metal artifact reduction (NMAR) [3], which is composed of segmentation and a normalizing operation.Zhao et al. proposed a method using a wavelet-based weighting function in the field of view [4], Zhang et al. modified metal regions on cross-sectional images by using projection data from two directions [5], and Abdoli et al. corrected projection data using weighted virtual sinograms [6].These methods partially reduced metal artifacts, but they also caused discrepancies and caused other problems such as streaking artifacts.M. Bal et al. conducted an adaptive filtering algorithm [7] and segmented reconstructed images into different material classes, but this method is dependent on parameter settings by manual operation.Alvarez et al. proposed a reconstruction algorithm based on projection data collected using two different energies [8].This approach is called Dual Energy (DE) methods, and many studies related to DE methods have been performed [9] [10].DE-CT has been applied to various artifacts reduction; however, there remain problems with hardware modifications and robustness due to the twice scans.T. Kano et al. focused on X-ray energy and proposed an iterative reconstruction algorithm from a deteriorated image and indicated that metal artifact can be suppressed by considering X-ray energy distribution [11].This work implies that metal artifacts can be theoretically reduced if enough X-rays reach the detector (if the main factor is beam hardening).Conversely, if the X-rays are saturated, it is impossible to correct these data through software modification.In this paper, we propose an optimization algorithm of rotation control for multi-axis X-ray CT to avoid saturation of X-ray intensities and reduce metal artifacts.More info about this article: http://www.ndt.net/?id=23727

Multi-axis X-ray computed tomography
Even if transmitted X-ray intensities are saturated in a certain direction because of overlapping metals, there could be other directions that contain regions that are not saturated.Therefore, we propose a rotation control algorithm for multi-axis X-ray CT.

Triaxial rotation mechanism
In this study, we added rotation angles and that describe the tilts of three-dimensional space on the stage in addition to a rotation angle θ that describes the angle of the stage (Figure 2).By changing and slightly and continually with the change of from to , we can perform a multi-axis forward projection while satisfying a certain level of angle conditions necessary for the cone beam reconstruction.
Rotation angles and are determined as follows.First, we put an object on the triaxial rotation mechanism.The objected was then scanned by a standard (single-axis) rotation while counting the number of metal regions in the projection data.
Because decreased metal area means that the metals are overlapped, we change the other one or two axes so that the metal area increases.Searching for the optimum angles and is performed at negative peaks of changes in the metal area during a standard projection.To shorten the search time, we used nine patterns as initial angles of and based on a combination of / , / , and / .In addition, the angle step in the search was set to / .After collecting several combinations angles , , and , we connect them smoothly using spline interpolation and complete the control function for the triaxial rotation.By conducting forward projection calculation based on this control function, it is expected that the metal area on the transmitted image decreases overall, and it leads to a reduction of saturated regions and metal artifacts.

Reconstruction algorithm
When projection data are recorded with angles of each axis in the multi-axis projection, we can calculate and obtaine reconstructed images based on the Feldkamp-Davis-Kress (FDK) algorithm modified for multi-axis scanning.This calculation is implemented just by back-projecting while applying a spatial correction.However, if there is no limitation on the variation amount or range of the multi-axis rotation, the projection data will be biased, and the reconstruction can be inaccurate.Therefore, we defined that the maximum search ranges of and are within the distance of / from their initial angles.

Simulation experiments
In this section, we conduct simulation experiments to verify our proposed method.

Numerical phantom
We prepared a three-dimensional numerical phantom composed of a resin, nine iron spheres, and an iron frame (Figure 3).The voxel size was × × and it is plane-symmetric in the central cross-section.At the height of 68 (and 188) and 88 (and 168), there is an iron frame but there are no iron spheres (Figure 3

Simulation conditions
In this simulation, we defined that the source-to-image distance is 1946 mm, the number of projection is 256, the X-ray source is a cone beam, and the tube voltage is 100 KeV.Also, we prepared a discrete X-ray energy distribution and X-ray attenuation coefficients for each energy to generate metal artifacts on simulation (Table 1).The X-ray attenuation coefficients for each element were calculated from mass attenuation coefficients found in the National Institutes of Standards and Technology (NIST) database [12].Figure 3 is the result of performing the conventional forward projection and the FDK algorithm.At all heights, metal artifacts were generated from the iron frame and the iron spheres.Notably, strong streak artifacts were generated at the height of 108 (Figure 4 (c)) and 128 (Figure 4 (d)), which contain iron spheres.

Multi-axis projection
Figure 5 is the graph of the changes in the metal area on transmitted images when performing the conventional (single-axis) projection.We can see that there are several negative peaks.For example, when the projection number is 0, the metal area was 5790 pixels (Figure 6 (a)).Meanwhile, by tilting both and to / , the metal area increases to 7184 pixels (Figure 6 (b)).By tilting both and to / , the metal area increases to 8093 pixels (Figure 6 (c)).As described above, we search and that maximizes the metal areas at each negative peak within the defined limits.

Results
In this experiments, we defined two thresholds for determining whether the peak is a negative peak to be corrected --threshold A and thresshold B are 6000 and 6500 pixels, respectively.The numbers of negative peaks are four for threshold A and eight for threshold B. Figure 7 shows the results of calculating the optimum and at each negative peak and connecting the regions between peaks smoothly using spline interpolation.The curves of threshold A are gently changing, whereas the curves of threshold B comparatively rapidly changing.Figutre 8 shows the changes in the metal area when performing forward projection while using curves in Figure 7 as control functions.The average of the metal areas at the conventional projection was about 7451 pixels, whereas those of two axes projection at threshold A and B and were about 10307 and 10338 pixels, respectively.It was confirmed that even if the number of negative peaks to be corrected increases by changing threshold, the amount of metal area does not extremely change.Figure 9 shows the results of three axes projection and back projection based on control functions shown in Figure 7.In cross-sectional images contains iron spheres (z = 108, 128), severe artifacts were effectively suppressed in our results compared to the FDK results (Figure 4 (c) (d)).In addition, at the height of 68, the outer shape of the resin can be observed.However, at the height of 88, the resin area became more blurred.This result means that the metal artifacts by iron spheres spread three-dimensionally and the saturation area decreased.Also, the results of threshold B contained more streak artifacts than the results of threshold A. It is thought that the remained streak artifacts are due to the change amount of the control functions.

Conclusion
We presented the concept of multi-axis X-ray CT and the optimization algorithm of its rotation control.By rotating objects around three axes while avoiding overlapping metals, both saturated regions in projection data and metal artifacts were suppressed.Although some streaks and dark stripes remained, it is thought that these artifacts can be minimized by using our iterative reconstruction algorithm or other metal artifact reduction methods.Our results illustrate that it is possible to inspect electronic devices with X-ray CT even if they contain numerous metals.

Figure 1 :
Figure 1: CT images containing metal artifacts.(a) is an electronic circuit and (b) is a cell phone.

Figure 2 :
Figure 2: The definition of two angles.
(b) (c)).At the heights of 108 (and 148) and 128 (center of the phantom), there is an iron frame and nine iron spheres (Figure3(d) (e)).

,Figure 3 :
Figure 3: The numerical phantom composed of a resin embedded with nine iron spheres and an iron frame.(a) is the volume rendering image, (b), (c), (d) and (e) are cross-sectional images at the heights of 68 (and 188), 88 (and 168), 108 (and 148) and 128 (center of the phantom), respectively.

Figure 4 :
Figure 4: The FDK results of the numerical phantom shown in Figure 3.

Figure 5 :Figure 6 :
Figure 5: The changes in the metal area accompanying forward projection

Figure 7 :
Figure 7: The results of calculating the optimum and .

Figure 8 :Figure 9 :
Figure 8: The changes in the metal area when performing forward projection based on control functions shown in Figure 7.