- Open Access
Comparison of ring artifact removal methods using flat panel detector based CT images
© Abu Anas et al; licensee BioMed Central Ltd. 2011
Received: 4 May 2011
Accepted: 17 August 2011
Published: 17 August 2011
Ring artifacts are the concentric rings superimposed on the tomographic images often caused by the defective and insufficient calibrated detector elements as well as by the damaged scintillator crystals of the flat panel detector. It may be also generated by objects attenuating X-rays very differently in different projection direction. Ring artifact reduction techniques so far reported in the literature can be broadly classified into two groups. One category of the approaches is based on the sinogram processing also known as the pre-processing techniques and the other category of techniques perform processing on the 2-D reconstructed images, recognized as the post-processing techniques in the literature. The strength and weakness of these categories of approaches are yet to be explored from a common platform.
In this paper, a comparative study of the two categories of ring artifact reduction techniques basically designed for the multi-slice CT instruments is presented from a common platform. For comparison, two representative algorithms from each of the two categories are selected from the published literature. A very recently reported state-of-the-art sinogram domain ring artifact correction method that classifies the ring artifacts according to their strength and then corrects the artifacts using class adaptive correction schemes is also included in this comparative study. The first sinogram domain correction method uses a wavelet based technique to detect the corrupted pixels and then using a simple linear interpolation technique estimates the responses of the bad pixels. The second sinogram based correction method performs all the filtering operations in the transform domain, i.e., in the wavelet and Fourier domain. On the other hand, the two post-processing based correction techniques actually operate on the polar transform domain of the reconstructed CT images. The first method extracts the ring artifact template vector using a homogeneity test and then corrects the CT images by subtracting the artifact template vector from the uncorrected images. The second post-processing based correction technique performs median and mean filtering on the reconstructed images to produce the corrected images.
The performances of the comparing algorithms have been tested by using both quantitative and perceptual measures. For quantitative analysis, two different numerical performance indices are chosen. On the other hand, different types of artifact patterns, e.g., single/band ring, artifacts from defective and mis-calibrated detector elements, rings in highly structural object and also in hard object, rings from different flat-panel detectors are analyzed to perceptually investigate the strength and weakness of the five methods. An investigation has been also carried out to compare the efficacy of these algorithms in correcting the volume images from a cone beam CT with the parameters determined from one particular slice. Finally, the capability of each correction technique in retaining the image information (e.g., small object at the iso-center) accurately in the corrected CT image has been also tested.
The results show that the performances of the algorithms are limited and none is fully suitable for correcting different types of ring artifacts without introducing processing distortion to the image structure. To achieve the diagnostic quality of the corrected slices a combination of the two approaches (sinogram- and post-processing) can be used. Also the comparing methods are not suitable for correcting the volume images from a cone beam flat-panel detector based CT.
Ring artifacts are common features in digital X-ray flat panel detector (FPD) based computed tomography imaging. Defective detector elements such as dead pixels in a CCD with non linear responses to the incoming intensity will create sharp rings in the reconstructions of width of one or two pixels. This type of sharp ring is also known as varying intensity rings. Similar artifacts also arise from the imperfect scintillator screens, i.e., the screens affected by scratch, dust or dirt . Mis-calibrated detector pixels, e.g., due to beam instabilities give rise to wider and less marked rings instead [2, 3]. It is reported that the ring artifacts can also arise from the monochromator , due to thermal processes in CCD , changes in temperature or beam strength  etc. As the gray value of the reconstructed images are affected by these ring artifacts, it is necessary to cancel them, otherwise, analysis after reconstructions, e.g., noise reduction or segmentation of image information, becomes significantly difficult .
Minimization of ring artifacts is possible by using flat-field correction , movable detector array [8, 9], adequate scanning protocols (e.g., dual gain calibration technique ). It is, however, difficult to completely avoid such artifacts and hence to achieve highest quality reconstruction solely by experimental measures . An effective way to eliminate the ring artifacts is the sinogram processing during the reconstruction [2–5, 11–21]. Another promising technique to remove these artifacts is the image space processing also known as post processing [6, 22–24]. In  a method is developed to correct the ring artifacts using a priori information of the attenuation coefficients in some areas of a CT slice. An algorithm is proposed in  that is based on the theory of inverse and ill-posed problems. The main idea to correct the ring artifacts is to minimize the Tikhonov's functional. A sinogram based ring removal method is proposed in  that is shown to be effective for correcting the 'regular' (the strength of ring artifact does not depend on the rotation angle) ring artifact structure. On the other hand, anisotropically attenuating objects (e.g., object has a large aspect ratio) and defective detector elements are responsible for 'irregular' ring artifact. The key concern of  is to suppress this type of ring artifacts.
It is, however, yet unknown which categories of algorithms is more effective in removing ring artifacts as no comprehensive performance analysis of the two categories of algorithms has been made from a common platform considering diverse complexity of the ring artifact problem. Furthermore, the ability of these algorithms in removing the ring artifacts from 3-D cone beam volume CT (CBVCT) images is also investigated. Moreover, different CT instruments (e.g., micro- and dental-CT) with different pixel size, detector area and, different tube current are also used to examine the performance of these methods. To the best of authors' knowledge, there have been no reports on the comparison of ring artifact removals from both micro-CT and dental-CT images. Finally, quantitative comparison is also provided to numerically evaluate the strength of the comparing methods in correcting the ring artifacts.
In this work, an extensive comparative study between the sinogram processing and post processing techniques is done from a common platform to reveal the strength and weakness of the representative algorithms selected from the two aforesaid categories.
A brief discussion on the reported ring elimination techniques whose performances are to be evaluated and compared is presented in this section. As the ring artifacts in the reconstructed tomographic image are due to the stripe artifacts in the sinogram, therefore, the sinogram based methods actually remove stripe artifacts from the sinogram image and then use the filtered back projection (fan or parallel beam reconstruction) algorithm to convert the corrected sinogram into a 2-D ring-free fan or parallel beam CT image. In multi-slice CT instruments, ring correction operation is performed on the sinogram image whereas in cone beam CT, an algorithm can be designed to work on the projection image (responses of the 2-D FPD for a particular view/angle). Unlike the fan or parallel beam based multi-slice CT, FDK algorithm  is used for the reconstruction in the cone beam geometry based CT. However, sinogram processing based techniques are often adapted to cone beam geometry based projection images by first constructing sinograms from the projections and then transferring back to the projection domain after correction [15–17, 19]. The differences between the multi-slice CT (fan or parallel beam CT) and cone beam CT are described in . A sinogram based ring artifact correction technique is presented in  that exploits the frequency property of a stripe-corrupted sinogram. Vertical stripes in a sinogram image will appear as high intensity along the horizontal line in Fourier transformed sinogram image. A computationally efficient numerical filter (Butterworth low-pass filter) is then utilized to suppress these horizontal line defects in the frequency domain. As significant image information is also located in the horizontal line of the Fourier transformed sinogram image, this method is not much reliable to remove the stripe artifacts from the sinogram image. An improved version of this method is recently published in  and this technique performs Fourier filtering on the coefficients of 2-D wavelet decomposed vertical detail band instead of on the original sinogram image. In [12, 5] efficient and fast methods have been proposed to remove the stripes by smoothing the sum curve computed from the corrupted sinogram and then normalizing the sinogram. The design of the smoothing filter, however, differs in the two approaches. Nevertheless, these methods fail to remove the varying intensity sharp rings, because the normalization procedure is inappropriate to eliminate this type of rings [5, 15–17]. Most recently, works based on center-weighted median filter  and morphological filters  and 1-D WMA/VWMA filters  have been reported to eliminate the ring artifacts from a tomographic image. But these techniques cannot suppress different types of ring artifacts effectively. Moreover, the algorithm in  is relatively computationally expensive.
A polar domain based post-processing algorithm is presented in  and it, at first, selects a region of interest (ROI) by separating the object from the image background and, then extracts the artifact template vector. Finally, the artifact template vector is subtracted from each row of the polar image in order to get the corrected polar image. Recently, two post-processing algorithms are reported in  and they are based on median and mean filtering of the reconstructed images but each working in different geometric planes, i.e., cartesian coordinate and polar coordinate. It is demonstrated in  that the ring artifact can be better removed in polar coordinate than that in the cartesian coordinate.
In this study, two algorithms from each of the two categories, i.e., total four algorithms are chosen to evaluate and compare their performances for various ring patterns generated by the CT imaging system and the objects. The first correction method is based on the sinogram processing and has been derived from . In fact, the algorithm in  removes the ring and radiant artifacts from the 3-D CBVCT images obtained using a 2-D flat panel digital detector. As the interest of this study is to compare the performance of the algorithms that can deal with parallel or fan beam projection images of multi-slice CT as well, some modifications are proposed to suit the algorithm in  to fan beam or parallel beam CT images. The second correction technique is the wavelet-Fourier method presented in  that uses both wavelet and Fourier filtering to remove the stripe artifacts from the sinogram images. The two post-processing algorithms that operate on the reconstructed images are taken from  and . As the ring artifact correction in polar coordinates (RCP) is more effective than that in the cartesian coordinates , therefore, only the RCP method from  is examined in our study. Finally, in this comparative study we also include our recently published sinogram based ring correction method . In the following, the proposed modification of the wavelet based method in  and the basic ideas behind the rest of the four algorithms are briefly explained. The limitations of each of the algorithm are also discussed alongside.
Modified wavelet plus normalization (MWPN) method
where, mod(j, L) is the remainder left after dividing the j by L. Generally in the 1-D wavelet operation, a downsample operation is performed after filtering (e.g., in this case equation (2)) the original signal. In this work, this downsampling operation on the filtered signal is not performed as it may exclude any bad pixels to be detected. The gray-scale plot of D k (n, j) for k = 4 is shown in Figure 1(f). Now, to detect the discontinuous points in D k (n, j) as suggested by the original work , a test is performed. If D k (n, j) ≤ m 1 - w 0 m 2 or D k (n, j) ≥ m 1 + w 1 m 2, then, the point (n, j) (where, 1 ≤ j ≤ j d and mod(j, L ) = mod(k, L)) is said to be discontinuous, otherwise, it is continuous. Here, , , m 1 = Mean(D k (n, j)), m 2 = SD(D k (n, j)), and, k 0 is an experimentally determined constant and is the normalized version of P k (n, j), i.e., . Here, the minimum value of P k (n, j) is P min and the maximum value of P k (n, j) is P max . SD(·) denotes the standard deviation operation. Now, a binary template matrix T k (n, j) of the same size as D k (n, j) is created, which contains either 1 or 0, i.e., if (n, j) contains discontinuity then, T k (n, j) = 0, otherwise it is 1. The distribution of the discontinuous points is shown in Figure 1(g). It is observed from this distribution that along the projections of the bad pixels the points are more discontinuous than those of the good pixels. As the target is to detect the bad pixel locations, the sum y k (j) of the gray values of each pixel j of the logically inverted matrix of T k (n, j) is calculated over each projection: , where, is the logically inverted matrix of T k (n, j). In the numerator n v is used to eliminate any effect of scaling on y k (j). The variation of y k (j) over j is shown in Figure 1(h). Now, a pixel j is detected as a bad pixel if y k (j) ≥ T HN , where, T HN is an experimentally determined threshold. The main drawback of this method is its failure of detecting the positions of the weak stripes. It is not possible to lower the value of T HN in order to detect the weak stripes, because doing this would falsely detect the edges of the sinogram image. Another problem of this technique is that due to the wavelet operation (please see equation 2), a single discontinuity at (n, j) = (n 0, j 0) in P k (n, j) leads to two high magnitudes in D k (n, j) at (n, j) = (n 0, j 0) and (n, j) = (n 0, j 0 + L) and therefore, if a stripe is located at the j = j 0-th pixel, then both the pixels at j = j 0 and j = j 0 + L are detected as bad pixels because of y k (j 0) ≥ T HN and y k (j 0 + L) ≥ T HN .
The operations of the algorithm on a particular subset sinogram (for k = 4) is shown in Figure 1. To detect the positions of all bad pixels, k must be varied from 1 to L (e.g., 4 in this case). To avoid the case of the stripes which were separated in the original sinogram, but form band stripes in the subset sinogram, the decomposition level (L) is varied from 1 to L max in order to detect all (isolated or band) types of stripes, where, L max is the maximum number of the decomposition levels. After detecting the positions of all stripe creating pixels, the correction is done by using the linear interpolation technique in the positions of the detected stripes only. The corrected sinogram thus obtained is denoted by P'(n, j).
where, N is the span factor.
Wavelet-Fourier (WF) method
Ring corrections using homogeneity test (RCHT) (Sijbers 2004) method
At first, a thresholding is performed on the reconstructed image (I) with a view to separate the object from the background . It is not crucial to select an accurate threshold (T ROI ) as the effect of an improperly chosen threshold will be compensated by the subsequent morphological operations (dilation + masked erosion + erosion + masked dilation). A binary image (B) is thereby generated that serves as a ROI to suppress the ring artifacts.
At first, the reconstructed CT image is transformed into polar coordinates.
A sliding window (column size W) is selected and a set of homogeneous rows that meet the homogeneity criterion (signal variance < threshold T) are detected and, an artifact template vector is then generated.
The line artifacts are corrected in the polar transformed image based on the set of artifact templates.
Finally, the polar image is transformed back into the cartesian coordinates to get the corrected 2-D reconstructed image.
It is to be noted that these operations are performed only on the pixels belonging to the ROI. In this method, the intensity of a ring is assumed to be constant throughout a ring structure because the same artifact template vector is subtracted from each row for suppressing the line artifact. This simple assumption, however, is not true for the often seen varying intensity rings and the performance of this algorithm is, therefore, expected to be not satisfactory for the removal of varying intensity ring artifacts.
Ring correction in polar coordinate (RCP)
Two thresholds (lower threshold T min and upper threshold T max ) are used so that no new artifacts are generated.
Median filtering is performed on the thresholded image in the radial direction.
To identify the ring artifact structures, the difference between the median filtered image and the thresholded image is computed. A second threshold (T RA ) is then used to ensure that the ring artifact structures pass the filtering while the bone structures are excluded.
Low-pass (mean) filtering is performed in the azimuthal direction in order to provide a difference image which contains only the artifact structures.
Finally, inverse transformation of the artifact image into cartesian coordinates yields the ring structures in this coordinate system. Then this artifact image is simply subtracted from the initial image to get the corrected image. The authors have shown that the method can remove ring artifacts from the C-Arm CT and micro-CT images [22, 23].
If varying intensity rings are present in a reconstructed CT image, then the difference image generated after step (3) expectedly contains the varying intensity rings. But the subsequent mean filtering of the difference image in the azimuthal direction certainly fails to hold the correct varying intensity ring structures in the difference image, because the varying intensity rings generally contain significant high frequency information and the mean filtering removes this information from the difference image. As the difference image does not always contain the appropriate ring structures, thus, the acceptable quality of the corrected image may not be achieved as it is obtained after subtracting the difference image from the original image.
Strength based ring correction(SBRC) method
In this method , at first the sinogram is windowed to create a sub-sinogram by keeping the pixel of examination at the center position in the sub-sinogram. The other pixels in the sub-sinogram are selected from a polyphase component of the sinogram. The polyphase concept is exploited to detect the band stripes correctly. The maximum number of polyphase levels (l m ) is equal to the maximum width of the band stripes in the sinogram. As stripes create discontinuity in the sinogram, a first-derivative-based algorithm is adopted to detect the stripes from a sub-sinogram. Exploiting the fact that the stripes generating from the defective detector elements are much stronger than those from the mis-calibrated detector elements, a derivative based mathematical index is calculated to measure the strength of the stripes. Finally, the strong and weak stripes are differentiated by comparing the index with two appropriately selected thresholds (e.g., r min and r max ). Two dimensional (2D) variable window moving average (2D-VWMA) and weighted moving average (2D-WMA) filters are used in a combined way to suppress the strong stripes because they require total reconstruction from the neighbors. On the other hand, the normalization method is used to eliminate the weak stripe artifacts from the sinogram. As this method classifies the ring artifacts into two groups and corrects each group by appropriate schemes, therefore, this method successfully suppresses different types of ring artifacts from the CT images.
Description of the data sources
The test images were acquired with a home made micro-CT and a dental-CT. The micro-CT consists of a CMOS FPD and a micro focus X-ray tube (L8121-01, Hamamatsu, Japan). For micro-CT experiments, two FPDs (C7943CA-02, C7942CA-02, Hamamatsu, Japan) were used. The FPDs consist of 1216 × 1220 and 2240 × 2240 effective matrix of transistors, and photodiodes with a pixel pitch of 100μ m and 50μ m, respectively, and a CsI:Tl scintillator. In one micro-CT experiment (bone image), we have used the detector (C7942CA-02) in 2 × 2 binning mode so that the active matrix size becomes 1120 × 1156. The CMOS FPD (Ray, Korea) in the dental-CT consists of 4096 × 1024 matrix of transistors, and photodiodes with a pixel pitch of 48μ m and a CsI:Tl scintillator. Here also we have used the FPD in 2 × 2 binning mode and, therefore, the active matrix size has become 2048 × 512. Both the micro- and dental-CT machines are based on cone beam geometry. Unfortunately, our CT system is not calibrated in Hounsfield unit (HU). Therefore, all the uncorrected CT images are first normalized in order to make the maximum pixel intensity 1.0 (arbitrary unit). Then we scale the corrected images by applying the corresponding normalization factor of the uncorrected images .
Results and Discussion
In this section, we test the performance of all the algorithms using some selective real CT images. All the methods use some parameters which need to be adjusted from image to image to achieve good results. For any method, parameter selection is an important point for effective removal of the ring artifacts. The first method (MWPN [12, 13]) uses four parameters: maximum number of decomposition levels (L max ), discontinuity index (k 0), threshold (T HN ) and span factor (N). L max is chosen in such a way that every stripe in the initial image gets isolated in any one of the subset sinograms. Generally, it is made equal to the maximum width of the band stripes. But even if a low value of L max (e.g., 1 or 2) is selected, it may work too. Because in the first stage (up to applying the normalization ), the aim is to remove the strong or varying intensity rings and they generally appear in at most two pixel width. The value of k 0 has an impact on the detection of the discontinuous points. A low value of k 0 leads to more points to be decided as discontinuous. The threshold T HN should be carefully selected so that it detects all the bad pixels but excludes the edge positions. Finally, the span factor (N) should be appropriately selected to eliminate the weak rings. The WF  has three parameters: decomposition level (L), mother wavelet and damping coefficient (σ). Here, the value of L is equal to the maximum stripe width. There are various choices available to select the mother wavelet, e.g., db1, db2, db3, db25, db31, db41, db42, db43 etc. Selection of a smaller length wavelet results in a low computation time, but at the cost of poor image quality. On the contrary, choosing longer length wavelets (e.g., db41, db42, db43) results in the best quality reconstructed image, but with higher computational burden. We prefer the second option to ensure good diagnostic quality of the reconstructed images. A low value of the damping coefficient (σ) is insufficient to eliminate the stripe information whereas a high value leads to a blurring effect in the tomographic images. The third method called the ring corrections using sliding window (RCHT)  has three parameters needed to be adjusted to obtain ring-free slices. They are threshold in ROI selection (T ROI ), column size (W) and homogeneity threshold (T). The selection of the first parameter is not critical as mentioned earlier. W should be chosen within the range [100-150] . On the other hand, the value of T is dependent on the ring artifacts. The less pronounced the line artifacts, the smaller the value of T can be chosen.
In case of the RCP  method, the filter width is selected as suggested in the original work, e.g., radial median filter width in polar coordinates, ; azimuthal filtering in polar coordinates, . On the other hand, the distance between the support points in the azimuthal direction for the polar coordinate is needed to be adjusted for our test CT images. We set equal to 0.7°, instead of 0.8°. In the original work , the distance between the support points in the radial direction (d RA ) for both the cartesian and the polar coordinates is determined from the scanner geometry. In our case, this parameter is set to 1.0 for the polar coordinate . The RCP method uses three thresholds (T min , T max and T RA ) for image segmentation and bone structure elimination. These three thresholds are considered in HU unit in the original work. Since our CT images are not adjusted in HU unit, therefore, these three thresholds are selected as mentioned in our previous work . In the following at first we present the comparative results of the MWPN, WF, RCHT and RCP methods and then in a separate section we show the results of our SBRC method.
Removal of varying intensity rings in a structural object
Ring artifact removal from micro-CT and dental-CT images
Ring artifact removal from multi-slice images
Removal of ring artifacts at the edges of high contrast object
Small high contrast object located exactly at the iso-center
Comparison of ring artifact correction methods using objective indices
Here, two numerical indices are used to quantify the corrected image quality. One is the conventionally used peak signal-to-noise ratio (PSNR) and the other is the mean structural similarity (MSSIM) . The first index PSNR is directly related to the intensity differences between the reference and corrected images. On the other hand, the latter is shown to be more correlated with the perceptual quality of an image. It considers luminance, contrast and structure similarity between the reference and corrected images to determine the value of the index. But evaluation of these two indices requires reference images, i.e., images free from ring and radiant artifacts. In CT imaging reference image is hardly available and, therefore, in this work one synthetic (computer simulated head phantom) sinogram image is used. In addition, two stripe-corrected versions of real FPD-CT sinogram images (rat abdomen and bone) are selected for comparison. These two images are obtained from a new and nearly error free FPD, so that the stripes present in the sinograms can be easily corrected by the state-of-the-art algorithm. Then, different types of stripe structures including single, band, stripes from defective and mis-calibrated detector elements are superimposed on the reference sinogram images to generate corrupted sinogram images. Note that the stripe structures added to the different reference images are also characteristically different. The comparing sinogram-processing methods are applied on these corrupted sinogram images and the post-processing methods, on the other hand, are applied on the CT images reconstructed from the corrupted sinograms. Now the above mentioned two indices can be calculated to quantify the visibility of errors between the reference and corrected CT images.
and X| P × Q and Y| P × Q are the reference and corrected CT images, respectively and, M I is the dynamic range of the reference image.
Quantitative performance of the comparing algorithms
Bone (figure 4(b))
WF with proposed pre-correction
RCHT with proposed pre-correction
RCP with proposed pre-correction
Although good results were demonstrated by the authors using the WF, RCHT and RCP methods [2, 6, 22, 23], these algorithms, however, when tested using our original, uncorrected CT images (e.g., Figures 3 and 5) the results found were not encouraging. Also the numerical results shown in Table 1 indicate the incapability of the WF, RCHT and RCP methods in properly correcting the ring artifacts. This poor performance may happen due to the presence of strong varying intensity rings in our CT images generated from the large area CMOS FPD and low X-ray exposure levels . Thus, some modifications may be needed in the WF, RCHT and RCP algorithms in order to suit these algorithms for such CT images. If the varying intensity rings can be removed anyway, then the corrected images by utilizing these three methods assure good diagnostic quality as demonstrated in Figure 6 and Table 1.
Performance summary of the comparing algorithms in some aspects (Yes = '√' and No = '×')
Is able to remove sharp varying intensity rings?
Is able to remove weak mis-calibrated rings?
Is able to remove radiant artifacts?
Is the corrected CT image free from blurring?
Is able to remove band ring artifacts?
Is diff. image is free from object information?
Is able to keep high contrast structure at iso-center?
Is applicable in dental-CT?
Is less sensitive to parameters setting?
Is able to suppress artifacts generally from all slices?
It is clear from Table 2 that none of the methods is suitable for correcting all types of the ring artifacts. A combination of two methods (e.g., MWPN and RCP) can be used to achieve the diagnostic quality of the corrected CT images. This type of combined (both sinogram- and post-processing algorithms) correction schemes are often installed in commercial CT scanners to obtain satisfactory results. But in one point all the methods are same, i.e., all these four methods cannot completely eliminate the ring artifacts from all slices of a 3-D CBVCT image. It is observed that some 2-D slices (e.g., a CT image in Figure 5(a)) in a CBVCT image may be severely corrupted and these algorithms particularly suited to multi-slice CT or processing CBVCT images slice by slice are in-appropriate to clean such slices.
The overall performance of a ring artifact removal technique can be evaluated by its effectiveness and the computation time it requires. The computation time will be an important factor for real time processing. A comparison of these four methods in terms of computation time reveals that the MWPN method requires the shortest time to generate a corrected images. The RCP method is faster than the WF method. On the other hand, excessive computational complexity in the RCHT method makes it the slowest amongst these four methods.
This paper has dealt with the performance comparison of different ring artifact correction algorithms (with FPD based CT images) selected from the two categories of reported techniques, namely, sinogram domain processing and post-processing. Real CT images from multiple FPDs have been used to test their effectiveness. As the ring artifacts appear in diverse forms, e.g., varying intensity and mis-calibration rings, band artifact, radiant artifact, rings in highly structural object, rings in between different contrast medium, therefore, none of the algorithms were found completely satisfactory for suppressing the ring artifact as clearly evident from Table 2. However, the overall performance of the MWPN method is better than the WF, RCHT and RCP methods as is evident from Table 1. This MWPN method is actually an improved version of the modified wavelet method. Incorporating the normalization technique with the proposed modified wavelet method effectively improves the image quality. The wavelet-Fourier method is particularly weak in suppressing the strong varying intensity ring artifacts and, on the other hand, the RCHT and RCP methods can reduce the strength of the varying intensity ring artifacts but fail to eliminate them completely. Therefore, low PSNR and MSSIM values are obtained for the WF, RCHT and RCP methods. If varying intensity rings are pre-corrected, then the performance of these methods, especially that of the RCP method becomes quite satisfactory as can be observed from Table 1. Band ring removal is still a critical issue in ring artifact research, and it is observed from our extensive analysis that only the RCP and a newly introduced SBRC method  can successfully remove this band ring artifact. It is also remarked that considering two different types of ring artifacts (e.g, varying intensity and mis-calibration) separately and adopting appropriate correction schemes for each type is one way to improve the accuracy of these correction methods. Moreover, it is noticed that a ring removal algorithm using neighborhood pixel information in 2-D space, e.g.,  is required to eliminate effectively the ring artifacts from all the slices of a 3-D CBVCT image.
This work was supported in part by the National Research Foundation (NRF) of Korea funded by the Korean government (MEST) (No: 2009-0078310).
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