Radiol Phys Technol (2013) 6:385–398 DOI 10.1007/s12194-013-0212-7

Assessment of bilateral filter on 1/2-dose chest-pelvis CT views Abdel Razzak Al-Hinnawi • Mohammed Daear Said Huwaijah

•

Received: 17 July 2012 / Revised: 3 April 2013 / Accepted: 4 April 2013 / Published online: 20 April 2013 Ó Japanese Society of Radiological Technology and Japan Society of Medical Physics 2013

Abstract A bilateral filter (BF) is a non-linear filter that has been proved to de-noise images without overrunning edges. Multi-slice computerized tomography (CT) may employ a BF to participate in dose reduction. This paper quantifies the role of the BF in achieving this objective on 1/2-dose CT. Two sets of CT images are acquired for the chest-pelvis at two different radiation doses. The BF was applied on the 1/2-dose CT images by use of various window sizes. Each time, a set of values of the BF range was fixed while the BF domain was modified. The goal was to observe the behavior of the BF on 1/2-dose CT images in comparison with full-dose CT images. The comparison was carried out by use of four co-occurrence matrix descriptors. Additionally, the peak signal-to-noise ratio (PSNR) and the mean square error (MSE) were reported. The study was applied to the sagittal, coronal, and axial CT views. The results showed that the impact of applying a BF varies among different CT views. The BF can retrieve only part of the signal being lost due to reduction of the radiation dose by one half. Yet, the BF improves the appearance of the 1/2-dose chest-pelvis CT examination. Thus, the BF can contribute to a 50 % dose reduction. A procedure for employing the BF on CT machines is proposed. The results

A. R. Al-Hinnawi (&)  M. Daear Electrical and Mechanical Engineering Faculty FMEE, Biomedical Engineering Department, Damascus University, Airport Street, PO. Box 86, Damascus, Syria e-mail: [email protected] S. Huwaijah Faculty of Medicine, Damascus University, Damascus, Syria S. Huwaijah Department of Radiology, Assads University Hospital, Mazzeh Street, Damascus, Syria

also showed that texture descriptors are similar to the PSNR and MSE in providing quantities for assessing medical image quality. Keywords Computerized tomography (CT)  Dose reduction  Bilateral filter  Co-occurrence matrix texture descriptors

1 Introduction Decreasing the radiation dose in multi-slice computerized tomography (CT) leads to a series of pitfalls such as a low signal-to-noise ratio (SNR) [1–3]. This results in decreasing image contrast, which leads to a deficiency in diagnostic observations. Therefore, if a reduction in the CT radiation dose is achieved without jeopardizing the CT image quality, this will be an important advance. A number of solutions have been published [3–6]. Some of these solutions involve the hardware of the CT machine such as optimizing the quality of the X-ray beam, or automatic exposure control (AEC) and optimal kV selection. Other solutions are based on software techniques as applied to either the projection space (i.e., sinogram) or the image space (i.e., reconstructed CT image). A bilateral filter (BF) was developed in 1998 by Tomasi and Manduchi [7]. It combines domain and range filtering in a preset window size. Optimum selection of the three BF variables (i.e., the BF range, domain, and window size) should lead to removal of noise from homogeneous structures while retaining the edges of objects in any arbitrary image. The BF function has been confirmed frequently by many researchers, such as Zhang and Gunturk [8] and Dong and Acton [9]. Therefore, since 1998, researchers

386

have tested the BF in various applications, wherever removing noise and preserving edges is required [8, 9]. This objective concerns medical imaging fields such as CT.

2 Literature review The study of employing a BF on CT images can be divided into two groups. The first group includes the BF algorithms that are run on the final CT image space [10–13]. Experiments in this group were applied to low-dose images acquired from a CT phantom [11, 13], abdominal CT [11], perfusion CT [10], abdomen dual-source CT [11], and cardiac CT [12]. The low-dose images were obtained by lowering of the tube current (i.e., mA) or the tube potential (i.e., kV). The comparison between low-dose and highdose images was done in terms of the time attenuation coefficient in the case of perfusion CT [10], of the line profile, of the peak signal-to-noise ratio (PSNR), or of the normalized mean square error (NMSE) [11–13]. Some researchers supported their results by asking the radiologist’s opinion about assessing the BF performance on lowdose images [11]. The second research group concentrated on testing the BF potential as applied to CT sinograms [14, 15]. Yu et al. [14] investigated the BF on sinograms of phantoms and on abdomen CT examinations as acquired with use of different reconstruction kernels, which leads to different noise levels in the final CT image. Manduca et al. incorporated the BF in a CT noise model in order to study the noise resolution properties on CT sinograms. This denoising process was tested on CT phantoms and patient abdominal CT studies acquired at different doses [15]. The noise-removal efficacy of the BF was evaluated by means of the modulation transfer function (MTF) and measurement of the noise level. Finally, Xu and Muller [16] incorporated the BF in the regularization process of an iterative reconstruction algorithm. The experiments were carried out on head and chest CT examinations for a child. The comparison between the reconstruction methods (i.e., with and without BF) was done based on the SNR and the time required by the computer to reconstruct the CT image. In this study, we tested the BF functioning on the final CT image space. We noted that the previous publications did not include the sagittal, coronal, and axial views of chest-pelvis clinical CT. Therefore, it is beneficial to determine the impact of the BF on this type of clinical CT examination. Also, it will be useful to investigate the BF behavior on various views acquired from CT examinations. Furthermore, using clinical half-dose CT images will make the results more practical than phantom study or CT images with added artificial noise in order to measure the role of the BF in CT dose reduction. Finally, we noted that

A. Al-Hinnawi et al.

co-occurrence matrix (CM) descriptors have not been used previously for assessment of the variation in image texture after a BF is applied to clinical CT examinations. This paper presents a discussion on the role of the BF variables (i.e., the BF range, the BF domain, and the BF window size) on the three views of a 50 % dose chestpelvis CT examination (axial, coronal, and sagittal). The discussion includes CM descriptors, PSNR, and MSE. This also allowed us to compare PSNR and MSE measures with CM texture metrics.

3 Theory 3.1 Bilateral filter The BF is a non-iterative adaptive smoothing filter that removes noise while it preserves the edges of the objects within an image. It was designed in 1998 to overcome the pitfalls associated with iterative methods [7]. Later, the functioning of the BF was thoroughly analyzed by researchers such as Elad [17] and Barash [18]. In comparison with iterative methods such as anisotropic diffusion or weighted least squares, the BF gives better results than do these iterative approaches, in terms of being fast and simple [7, 17, 18]. The BF combines the geometric closeness (i.e., filter domain) and photometric similarity (i.e., filter range) among pixels in an N 9 N mask (i.e., the BF window size) in order to remove noise without affecting sharp details. Equation (1) describes the BF mathematics: IBF ðx; yÞ ¼

ð^x;^yÞþN kx^xk2 þky^yk2 ðIðx;yÞIð^x;^yÞÞ2   1 X 2r2 2r2 d r e e I ðx; yÞ; k x;y ¼ ð^x;^yÞN

ð1Þ

where k is a normalization constant given by: K¼

ð^xX ;^yÞþN

e



kx^xk2 þky^yk2 2r2 d



e

ðIðx;yÞIð^x;^yÞÞ2 2r2 r

:

ð2Þ

x;y ¼ ð^x;^yÞN

The first BF parameter is rr, which determines the filter range as illustrated in Eq. (3), whereas Eq. (4) states that the filter domain is determined by the second parameter, denoted by rd. e e

ðIðx;yÞIð^x;^yÞÞ2 2r2 r

;

ð3Þ

kx^xk2 þky^yk2 2r2 d

:

ð4Þ





The geometric spread of the BF is controlled by rd. As rd is increased, more neighbors are combined for diffusion, resulting in higher smoothing, whereas, rr represents the photometric spread of the BF. Only pixels with an intensity

Assessment of bilateral filter on 1/2-dose

387

percentage difference less than rr are processed, whereas those higher than rr are not. In summary, the BF has three variables. These are the BF window size (W), the filter range controlled by rr, and the filter domain determined by rd. 3.2 Noise measures The PSNR and the MSE are common parameters that are used for assessment of the variations in medical image quality after any processing step [20]. Equation (5) describes the MSE and Eq. (6) describes the PSNR. MSE ¼

M X N 1 X ðf1 ði; jÞ  f2 ði; jÞÞ2 ; MN i¼1 j¼1

PSNR ¼ 10 log10

ð L  1Þ 2 ; MSE

ð5Þ

ð6Þ

where M and N are the number of rows and columns in the image; L is the number of gray levels in the image; i and j are variables; and f1 and f2 are the input and output images, respectively. 3.3 Co-occurrence matrix measures Co-occurrence matrix (CM) descriptors are a branch of image texture metrics [19]. The CM examines the relative position of pixels with respect to each other (i.e., the spatial distribution) in an image. The repetition of gray levels (i.e. gray levels occurrence) is guided by the preset neighborhood connectivity conditions. After a CM is generated for an image, a set of descriptors can be calculated that describes the overall texture of the original image. We used four CM descriptors: correlation, uniformity, entropy, and homogeneity. They are described by the following expressions: Homogeneity ¼

K X K X i¼1 j¼1

Correlation ¼

Pij ; 1 þ ji  jj

ð7Þ

K X K X i¼1

ði  mr Þðj  mc ÞPij ; ra rb j¼1

ð8Þ

where ra & rb 6¼ 0; Entropy ¼ 

K X K X

Pij log2 Pij ;

ð9Þ

i¼1 j¼1

Uniformity ðEnergyÞ ¼

K X K X

P2ij ;

ð10Þ

i¼1 j¼1

where k is the number of both rows and columns in the CM; i and j are the discrete gray levels; Pij is the probability for a discrete value i to occur besides the discrete

value j; mr and mc are the means of gray levels in a row and column, respectively; and ra and rb are the standard deviations of gray levels in a row and column, respectively. Equation (7) states that the value of ‘‘Homogeneity’’ is in the range ‘‘0’’ to ‘‘1’’. When the homogeneity is ‘‘1’’, this means that all gray levels in the image have equal occurrence, leading to a diagonal CM; and ‘‘0’’ means that the CM is far beyond being diagonal [19]. Therefore, as the noise is increased in the image, the meaningful gray levels occurrence decreases; this, in turn, gives low ‘‘Homogeneity’’. The ‘‘Correlation’’ varies in the range from -1 to ?1, as explained in Eq. (8). This range corresponds to either a perfect negative or a perfect positive correlation between pixels [19]. Hence, the increased noise pattern in any arbitrary image should exhibit a low ‘‘Correlation’’ among its pixels. The maximum expected value for ‘‘Entropy’’ is 2 log2 K [Eq. (9)]. The maximum value occurs when all Pij are equal, whereas, it is ‘‘0’’ when all Pij are zeros [19]. Therefore, the increased noise pattern in an image should lead to an increase in the noise-intensity occurrence close to the other meaningful gray levels occurrence in the image (i.e., image graininess). This, in turn, leads to low ‘‘Entropy’’. The results for ‘‘Energy’’ should be in the range ‘‘0’’ to ‘‘1’’ [Eq. (6)]. When the ‘‘Energy’’ is ‘‘1’’, this means that the image is a constant gray-level image and the CM has only one single repetition value, whereas, when the ‘‘Energy’’ is ‘‘0’’, this represents an image with no ‘‘Energy’’ due to the presence of all the gray-scale values in the image [19]. Therefore, as the noise pattern is increased, the image tends to have the gray levels co-occurrences being concentrated on a small number of gray levels, and the ‘‘Energy’’ increases.

4 Materials and methods Figure 1 is a block diagram of the research methodology. The BF window size (W) was set to 3 9 3, 5 9 5, 7 9 7, or 9 9 9. We believe that these sizes should encompass a substantial amount of noise patterns in any CT image. At each window size, the BF was applied to a CT low-dose utilizing different values of rd and rr. The values of rd were changed in the following steps: 0.25, 0.5, 0.75, 1, 1.5, 2, 2.5, 3, 3.5, and 4. We cannot test values rd [ 4 because this would exceed the range of the difference between the center pixel and the most distant pixel in the case of the largest window size (i.e., 9 9 9). On the other hand, the values of rr were altered in the following intervals: 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, and 1. These small values assure that the BF is operating in the correct

388

zone (i.e., it will not operate like a non-adaptive smoothing filter). The experiments were to choose a fixed value for rr, then to apply the BF to the above-mentioned different values for rd. These experiments were done on 100 mA CT images. Each time after the BF was applied at certain combinations of values of rr and rd, the co-occurrence matrix CM was generated; then the four descriptors in Eqs. (7–10) were calculated. We chose the 8-neighborhood connectivity for the CM generation because it is the general situation [19]. The PSNR and MSE in Eqs. (5, 6) are also calculated on 100 mA CT images after the BF was applied at certain combinations of values of rr and rd. The BF was not applied on the 200 mA images, but the CM descriptors were measured. We used the resulting values as references to see how close the BF can bring each CM metrics of the 100 mA CT image toward its value on the 200 mA CT image. The experiments were implemented under the supervision of the Radiology Research Committee and the Institutional Review Board at the Damascus University Assad Hospital. A 300 mA chest-pelvis CT examination was divided into two parts (i.e., 200 ? 100 mA) in order to yield two groups of CT images acquired with use of 16 slices of a ‘‘Aquilion’’ TOSHIBA Helical CT system (TOSHIBA, Tokyo, Japan). Thus, the set of 200 mA images will be a 67.6 % dose reduction in comparison with the 300 mA CT settings, whereas the set of 100 mA images will be a 33.3 % dose reduction in comparison with the 300 mA CT settings. Both groups were acquired without the use of AEC. The first group was obtained at 200 mA tube current (effective mAs = 160), whereas in the second group, the tube current was selected to be 100 mA (effective mAs = 80). Both groups were acquired at the same display field of view (DFOV = 390.6 mm) and range = 590 mm, so that both sets had the same number of slices. All other acquisition parameters were set so that they were similar (e.g., rotation

Fig. 1 Research methodology block diagram

A. Al-Hinnawi et al.

time = 0.75 s, total scan time = 31.25 s, tube potential = 120 kV, window level = 40 HU, window width = 400 HU, image thickness = 5 mm, reconstruction interval = 5 mm, pitch factor = 1.4). The resulting volume CT dose index (CTDIvol) were 21.2 and 10.6 mGy, whereas the resulting dose-length products (DLPs) were 1.33 Gy cm and 663.2 mGy cm, respectively. Therefore, all of the 100 mA images can be considered as having a 50 % reduction in the radiation dose in comparison to the 200 mA images. The 200 mA CT images are used as references, as explained in Fig. 1. Consequently, in this paper and from this point on, we use the terms ‘‘full dose’’ and ‘‘half dose’’ to indicate to the 200 mA and the 100 mA CT images, respectively. However, it is important to note that they are the 67.6 and the 33.3 % dose reduction in comparison with the 300 mA CT setting. Both groups were reconstructed to have sagittal, coronal, and axial views of the chest-pelvis examination. Later, 80 sagittal, 80 coronal, 220 axial adjacent slices were selected for the experiments. Figures 2, 3, and 4 show examples of CT images. There is a slight misalignment between the 200 mA and 100 mA CT images for the same slice. This is due to unavoidable variation in breath holding by the patient during image acquisition. These experiments were carried out with use of MATLAB version 7.12 R2011a installed in an HP portable computer (Intel processor Core-2-due 2.6 GHz, RAM = 4 GByte, Cash Memory = 3 MByte). The average time required for applying the BF on a 512 9 512 CT image was about 25 s. The experiments were applied to the CT gray-scale values.

5 Results Figures 5, 6, 7, 8, 9, 10 illustrate the results of calculating the CM descriptors, PSNR, and MSE of the 50 % dose CT

Assessment of bilateral filter on 1/2-dose

389

Fig. 2 Axial-pelvis CT images. a 200 mA, b 100 mA

Fig. 3 Sagittal chest-pelvis CT images. a 200 mA, b 100 mA

images in Figs. 2, 3, 4 after being filtered by the BF at different rd and rr values. Each figure has four curves showing one quantity (i.e. PSNR, MSE, or a CM descriptor) calculated after the BF was used at four different window sizes. Figures 7, 8, 9, and 10 also contain a straight line that shows the CM descriptor’s value of the full-dose image (i.e., 200 mA) as a reference. 5.1 Noise measures 5.1.1 Peak signal-to-noise ratio (PSNR) Applying the BF should remove the noise leading to improvement in the PSNR. This is confirmed in Fig. 5a–f,

which shows that applying the BF resulted in an increase in the PSNR. The curves in these figures indicate that the optimum range of values for the rd for all CT views is 0.25 \ rd \ 1, whereas the optimum range of values for rr is 0.05 B rr B 0.5. Selecting rd outside this limit (i.e., rd [ 1) will lead to loss of the BF feature on low-dose CT images, as illustrated in Fig. 5b. These two optimum rd and rr ranges (i.e., 0.25 \ rd \ 1 and 0.05 B rr B 0.5) correspond to an increase in the PSNR up to approximately 1.2, 0.9, and 0.6 dB of the half-dose axial, coronal, and sagittal CT views, respectively. These results are associated with gains in the PSNR up to approximately 32, 23, and 15 %, respectively. Finally, the figures show that the effect of the BF window size starts at rd [ 1 for all CT

390

A. Al-Hinnawi et al.

Fig. 4 Coronal chest-pelvis CT images. a 200 mA, b 100 mA

Fig. 5 PSNR values from BF half-dose images at different values of rr, rd, and W for all CT views. a, b Axial, c, d coronal, e, f sagittal

Assessment of bilateral filter on 1/2-dose

391

Fig. 6 MSE values from BF half-dose images at different values of rr, rd, and W for all CT views. a, b Axial, c, d coronal, e, f sagittal

views. When rd [ 1, a greater window size leads to a greater loss of the BF linearity (i.e., the BF starts to behave similar to a linear smoothing filter in which both edges and noise are blurred equally).

respectively. Also, as in PSNR, the impact of the BF window size starts at rd [ 1 for all CT views.

5.1.2 Mean square error (MSE)

5.2.1 CM image homogeneity

Theoretically, any low-dose CT image should contain a higher percentage of noise. Applying the BF should remove the noise leading to a lower MSE. This is proved in Fig. 6a–f, which shows that applying the BF resulted in a decrease in the MSE for all CT views. As in the PSNR, the MSE curves indicate that the optimum range of values for the rd for all CT views is 0.25 \ rd \ 1, whereas the optimum range of values for rr is 0.05 B rr B 0.5. Selecting rd outside this range (i.e., rd [ 1) will lead to loss of the BF feature on low-dose CT images, as illustrated in Fig. 6b. These two optimum rd and rr ranges (i.e., 0.25 \ rd \ 1 and 0.05 B rr B 0.5) correspond to an MSE percentage declines up to 33, 22, and 15 % of the half-dose axial, coronal, and sagittal CT views,

Because applying the BF will remove the noise from the image, the homogeneity of the image should increase. Figure 7a–f confirms this. They show that the high-dose CT images exhibit a higher homogeneity than do the 1/2dose CT images. Applying the BF improves the homogeneity. If we consider the intersection between the value of the homogeneity of the full-dose image (i.e., 200 mA) with its value for the half-dose image (i.e., 100 mA) as a reference point, the optimum range of values for the rd for all CT views is 0.25 \ rd \ 1, whereas the optimum range of values for rr is 0.05 B rr B 0.5. These two optimum rd and rr ranges (i.e., 0.25 \ rd \ 1 and 0.05 B rr B 0.5) are associated with improving the homogeneity up to approximately 5.5, 12.5, and 7 % of the half-dose axial, coronal,

5.2 Co-occurrence matrix descriptors

392

A. Al-Hinnawi et al.

Fig. 7 Homogeneity values from BF half-dose images at different values of rr, rd, and W for all CT views. a, b Axial, c, d coronal, e, f sagittal

and sagittal CT views, respectively. On the other hand, the role of the BF window size begins at rd [ 1 for all CT views. 5.2.2 CM image correlation Because low-dose CT images exhibit an increased noise pattern, such images will have a low correlation among their pixels. This is proved in Fig. 8a–f, which shows that applying the BF will improve the correlation among pixels of the half-dose images (i.e., 100 mA) toward the full-dose image (i.e., 200 mA). Like the situation for homogeneity, the optimum range of values for the rd for all CT views is 0.25 \ rd \ 0.75, whereas the optimum range of values for rr is 0.05 B rr B 0.5. These two optimum rd and rr ranges (i.e., 0.25 \ rd \ 0.75 and 0.05 B rr B 0.5) lead to enhancing the correlation of about 1.4 %, 1.2 %, 1.2 of the half-dose axial, coronal, and sagittal CT views. The role of the rr is to increase the noise-removal efficacy of the BF, whereas the role of the BF window begins at rd [ 1.5 for all CT views.

5.2.3 CM image entropy The increased noise pattern in the half-dose CT image will lead to more varied gray-level co-occurrences than does the high-dose CT image. This, in turn, leads to low entropy. Figure 9a–f illustrates this fact. Applying the BF results in increase in the entropy because of noise removal. As with the situation of homogeneity and correlation, the optimum range of values for the rd for all CT views is 0.25 \ rd \ 0.75, whereas the optimum range of values for rr is 0.05 B rr B 0.5. Using these two optimum rd and rr ranges (i.e., 0.25 \ rd \ 0.75 and 0.05 B rr B 0.5) should enhance the entropy up to approximately 1.7, 9, and 8 % of the half-dose axial, coronal, sagittal CT views, respectively. For values rd [ 0.75, the BF starts to lose its feature, as shown in Fig. 9b, d, f. Again, the role of the rr is to increase the noise-removal efficacy of the BF, whereas the role of the BF window begins at rd [ 0.75. After that (i.e., rd [ 0.75), the BF behavior on half-dose CT images becomes proportionally dependent on the window size W.

Assessment of bilateral filter on 1/2-dose

393

Fig. 8 Correlation values from BF half-dose images at different values of rr, rd, and W for all CT views. a, b Axial, c, d coronal, e, f sagittal

5.2.4 CM image energy As explained in the ‘‘ Sect. 4’’ of this paper, the 50 % dose CT image should exhibit low energy due to a higher percentage of noise. As the noise is decreased by the BF, the energy should be enhanced, as shown in Fig. 10a–f. As with the situation of previous CM descriptors, the optimum range of values for the rd for all CT views is 0.25 \ rd \ 0.5, whereas, the optimum range of values for rr is 0.05 B rr B 0.5. These two optimum rd and rr ranges (i.e., 0.25 \ rd \ 0.5 and 0.05 B rr B 0.5) lead to enhancement of the entropy of the low-dose CT up to 3, 10, and 6 % of the half-dose axial, coronal, sagittal CT views, respectively. The role of the BF window begins at rd [ 1. After this value, the BF starts to depend on the increase of the window size W.

6 Discussion Our experiments were tested on the selected half-dose CT images from the chest-pelvis examination. Results similar

to those shown in Figs. 5, 6, 7, 8, 9, and 10 were obtained. For all CT views, the BF window size has no effect as long as rd B 1 and rr B 0.5 are used. Table 1 lists the optimum zone for the BF domain rd and BF range rr for all CT views as concluded from Figs. 5, 6, 7, 8, 9, and 10. The table shows that the general setting for rr and rd is to set their values within the ranges 0.05 B rr B 0.5 and 0.25 \ rd \ 1. These two limits guarantee that the impact of applying BF is still in the useful zone (i.e., still working as a non-linear filter in suppressing noise and preserving edges). Afterwards (i.e., rd [ 1 and rr [ 0.5), the BF starts to lose its property (i.e., it starts to smooth noise and edges equally) on the half-dose CT images, as shown in PSNR, MSE, and entropy (i.e. Figs. 5, 6, 9). Also, the BF behavior starts to be dependent on the window size when rd [ 1 and rr [ 0.5 for all CT views. According to Figs. 5, 6, 7, 8, 9, and 10, using these two values (i.e. rr = 0.5 and rd = 1), Table 2 lists the maximum possible gain for each image metric due to applying the BF to different CT views. The experiments and the results indicate the following findings: First, it is clear that the impact of noise removal

394

A. Al-Hinnawi et al.

Fig. 9 Entropy values from BF half-dose images at different values of rr, rd, and W for all CT views. a, b Axial, c, d coronal, e, f sagittal

by the BF varies with the type of CT view (Table 2; Figs. 5, 6, 7, 8, 9, 10). For example, applying the BF improves the PSNR by various amounts on different CT views (32, 23, 15 %), although the amount of noise due to dose reduction is similar (i.e. all views are 1/2-dose CT views). This variation in the amount of PSNR improvement among CT views can be attributed to the different sizes of structures within different CT views. The axial views, which usually encompass a large area of tissues, exhibit the highest PSNR improvements (i.e., 32 %). In contrast, the sagittal views, which encompass a thinner area of tissues, exhibit the lowest PSNR improvement (i.e., 15 %). Therefore, it is important to indicate that CT researchers may need to consider the type of CT view when they test the BF as an image-space tool for CT dose reduction. This finding has not been reported previously [10–13]. The second finding is that the selection of rr and rd values is controlled by the observer. For example, Figs. 11 and 12 show the full dose (i.e., 200 mA), half dose (i.e., 100 mA), and two BF half-dose images processed at two different pairs of values of rr and rd. Figures 11a–d show

regions of interest (ROIs) including the sagittal chest-pelvis vertebral region, whereas Fig. 12a–d show ROIs including part of the liver extracted from axial CT views. We cannot tell which is better, Fig. 11c or d, nor Fig. 12c or d. The observer is the only judge in this matter. The observer is a radiologist (not an image-processing specialist). It is well known that observers also may have different opinions among themselves. In other words, choosing the optimum rr and rd values may depend on each CT slice and each CT view (and is likely to be dependent on both the type of CT examination and the radiologists, although this was not tested in this paper). For example, in Figs. 11c, d and 12c, d, the selection of rr and rd for observing the liver may differ from those for observing the vertebrae. This point also has not been reported previously [10–16]. The third finding concerns the overall BF performance. The results we report here (Table 2; Figs. 5, 6, 7, 8, 9, 10, 11,12) are in agreement with other research work, that the BF can be used as an image-space tool for de-noising of low-dose CT images [10–16]. Numerically, for the 1/2-

Assessment of bilateral filter on 1/2-dose

395

Fig. 10 Uniformity values from BF half-dose images at different values of rr, rd, and W for all CT views. a, b Axial, c, d coronal, e, f sagittal Table 1 BF optimum parameters at each image metric rr

rd

Table 2 The highest gain for image metrices when rr = 0.5 and rd = 1 for different CT views

CM texture metrics Energy

0.05 B rr B 0.5

0.25 \ rd \ 0.5

Entropy

0.05 B rr B 0.5

0.25 \ rd \ 0.75

Correlation

0.05 B rr B 0.5

0.25 \ rd \ 0.75

Homogeneity

0.05 B rr B 0.5

0.25 \ rd \ 1

Noise metrics PSNR

0.05 B rr B 0.5

0.25 \ rd \ 1

MSE

0.05 B rr B 0.5

0.25 \ rd \ 1

dose CT views in this research, the experiments (Table 2) showed that the BF can raise the PSNR of the axial views by 32 %, homogeneity by 5 %, correlation by 1.7 %, and entropy by 1.5 %, whereas it minimizes the MSE by 33 % and the energy by 9 %. These results change for other CT views (i.e., sagittal and coronal in Table 2). However, in theory, the 1/2-dose CT views should have a 50 % lack of signal in comparison to the full-dose CT views (i.e., 200 mA). This means that the BF is able only to retrieve a

Axial CT view

Coronal CT view

Sagittal CT view

*-9 % *1.7 %

*-18 % *11 %

*-13 % *9 %

CM texture metrics Energy Entropy Correlation

*1.7 %

*1.5 %

*1.5 %

Homogeneity

*5.5 %

*12 %

*7 %

Noise metrics PSNR

*32 %

*23 %

*15 %

MSE

*-33 %

*-22 %

*-15 %

part of the signal that is lost in the 1/2-dose CT chest-pelvis examination. This, for example, is illustrated in Fig. 13, which shows the cumulative histograms of the four images in Fig. 12. Figure 13 demonstrates that applying the BF yielded an enhancement of the 1/2-dose CT images (i.e., 100 mA) toward the full dose, but it did not match the appearance of the full dose. It is important to mention that

396

the impact of the BF could be improved further if the AEC is used. This is because the AEC, which is a common practice in CT clinics nowadays, leads to a decrease in the amount of noise in the CT images. For the first and second findings which are mentioned above, we suggest the following scenario. The BF is incorporated as separate dedicated software in CT machines. This software should be designed so that the user (radiologist) may adjust rr and rd in backward or forward steps at any time and observe the on-line impact of applying the BF on the low-dose CT image (e.g., similarly to the preset CT window level and width functions). The BF software may be considered as a supplementary software to be used when low-dose CT images are needed. For the third finding, we can only suggest adding another supportive technique. Also, there is a need to run clinical trials on clinical CT findings (i.e., diseases) to

A. Al-Hinnawi et al.

judge to what extent this partial recovery of the SNR can be useful in extending the diagnostic value of 1/2-dose CT images. The fourth finding in this paper is related to medical image-processing science. The CM texture descriptors (i.e., CM homogeneity, uniformity, entropy, and correlation) can be used as metrics for quantifying the performance of the BF, similar to the MSE and PSNR metrics which are in common use [11–13, 16]. Furthermore, the CM descriptor has the advantage that it allows comparison with other images for reference (Figs. 7, 8, 9, 10). In other words, the texture descriptors can be calculated on full-dose and halfdose CT images separately. This is not possible for the PSNR and MSE, as illustrated in Eqs. 5 and 6. Although it is clear from Table 2 that the MSE and PSNR are more sensitive to variation in noise than are the CM texture descriptors, the CM metrics have the advantage of being

Fig. 11 a 200 mA image, b 100 mA image, c BF at rr = 0.2 and rd = 0.75, d BF at rr = 0.5 and rd = 1

Assessment of bilateral filter on 1/2-dose

397

Fig. 12 a 200 mA image, b 100 mA image, c BF at rr = 0.3 and rd = 0.5, d BF at rr = 0.4 and rd = 0.75 Fig. 13 Cumulative histograms of the liver ROI in Fig. 12a–d

more related to the appearance of the internal regions of objects in an image [19] than are the PSNR and MSE, which are global image metrics of noise percentage in the image. In comparison with published papers [10–16], this research sustains other research work that the BF can be used as an image-space tool to de-noise low-dose CT images. This should facilitate dose reduction. However, the experiments described in this paper were performed on all views of a chest-pelvis CT examination, whereas other published research was performed on only axial or phantom CT images [10–16]. Also, our research was performed on real 1/2-dose CT images, whereas there has been no similar study reported. Also, this paper introduces the use of texture descriptors for objective metrics of image quality. Finally, it is important to mention that one can expect similar results for CT images which are acquired at a higher percentage of dose reduction (e.g. 75 %). Furthermore, the BF may be useful for a CT dose reduction lower than 50 %, as in the work by Giraldo et al. [10]. However, according to the experiments described in this paper, if a lower tube current was used (i.e., less than 100 mA), the percentage of noise removal by the use of the BF is expected to decrease. The research in this field will keep progressing [21]. These research efforts may lead to the use

of the BF to contribute to making CT low-dose examinations be useful diagnostic tools.

7 Conclusions In this study, we tested the BF capability to remove noise from 50 % dose chest-pelvis CT views. The resulting BF half-dose CT images were assessed by PSNR, MSE, and CM texture descriptors. The results showed that: 1. 2. 3.

4.

The BF window size is not critical at rd B 1 and rr B 0.5 for all CT views. The impact of noise removal by the BF varies with the type of CT view. The selection of rr and rd depends on the CT slice and CT view being examined. The selection of these parameters can only be done by the radiologist. The BF can recover only a part of the signal lost due to reduction of the radiation dose by half. Yet, the results showed that the BF can be used to enhance the appearance of the 1/2-dose CT image.

The CM texture descriptors proved to be similar to the PSNR and MSE in providing measures for image quality assessment. The PSNR, MSE, and CM texture descriptors all showed that the BF is capable of raising the quality of

398

A. Al-Hinnawi et al.

the 50 % dose image. This means that the BF is a successful prospective tool that can contribute to dose reduction in routine CT examinations. Conflict of interest of interest.

The authors declare that they have no conflict

References 1. Bushong SC. Radiologic Science for technologist: physics, biology, and protection. 9th ed. Missouri: MOSBY; 2008. p. 367–93. 2. Sprawls P. CT image detail and noise. Radiographics. 1992;12:1041–6. 3. Yu L, Liu X, Leng S, Kofler JM, Giraldo JR, Qu M, et al. Radiation dose reduction in computed tomography: techniques and future perspective. Imaging Med. 2009;1:65–84. 4. McCollough CH, Bruesewitz MR, Kofler JM. CT dose reduction and dose management tools: overview of available options. Radiographics. 2006;26:503–12. 5. Perisinakis K, Papadakis AE, Damilakis J. The effect of X-Ray beam quality and geometry on radiation utilization efficiency in multidetector CT imaging. Med Phys. 2009;36:1258–66. 6. Li T, Li X, Wang J, Wen J, Lu H, Hsieh J, et al. Nonlinear sinogram smoothing for low-dose X-ray CT. IEEE Trans Nucl Sci. 2004;51:2505–13. 7. Tomasi C, Manduchi R. Bilateral filtering for gray and color images. In: IEEE International Conference on Computer Vision, 4–7 Jan., Bombay-India. 1998; p. 839–46. 8. Zhang M, Gunturk BK. Multiresolution bilateral filtering for image denoising. IEEE Trans Image Process. 2008;17:2324–33. 9. Dong G, Acton S. On the convergence of bilateral filter for edgepreserving image smoothing. IEEE Signal Process Lett. 2007;14:617–20. 10. Giraldo JR, Leng S, Yu L, McCollough C. 20-Fold dose reduction using a gradient adaptive bilateral filter: demonstration using in vivo animal perfusion CT. Med Phys. 2010;37:3372.

11. Giraldo JR, Kelm ZS, Guimaraes LS, Yu L, Fletcher JG, Erickson BJ, et al. Comparative study of two image space noise reduction methods for computed tomography: bilateral filter and nonlocal means. In: 31st annual international conference of the IEEE EMBS, Minneapolis-USA, 2–6 Sept. 2009;3529–32. 12. Steckmann S, Kachelrieß M. Blooming artifact reduction for cardiac CT. In: Nuclear Science Symposium Conference Record (NSS/MIC) IEEE. 30th Oct.–6th Nov. Knoxville-USA. 2010;2030–35. 13. Huang J, Ma L, Liu N, Feng Q, Chen W. Projection data restoration guided non-local means for low-dose computed tomography reconstruction. In: IEEE international symposium on biomedical imaging: from nano to macro, 30th March–2nd April, Chicago-USA. 2011;1167–70. 14. Yu L, Manduca A, Trzasko J D, Khaylova N, Kofler JM, McCollough CM, et al. Sinogram smoothing with bilateral filtering for low-dose CT. In: Proceedings of SPIE. 2008; Vol. 6913 691329–1. doi:10.1117/12.772084. 15. Manduca A, Yu L, Kofler JM, McCollough CM, Fletcher JG, Trzasko JD, et al. Projection space denoising with bilateral filtering and CT noise modeling for dose reduction in CT. Med Phys. 2009;36:4911–9. 16. Xu W, Mueller K. A performance-driven study of regularization methods for GPU-accelerated iterative CT. 10th fully threedimensional image reconstruction in radiology and nuclear medicine, In: 2nd High Performance Image Reconstruction Workshop, September, Beijing-China. 2009;20–3. 17. Elad M. On the origin of the bilateral filter and ways to improve it. IEEE Trans Image Process. 2002;11:1141–51. 18. Barash D. Fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation. IEEE Trans Pattern Anal Mach Intell. 2002;24:844–7. 19. Gonzales R, Woods R. Digital image processing. 3rd ed. New Jersey: PEARSON Prentice Hall; 2008. p. 822–36. 20. Verma A, Sharma B. Comparative analysis in medical imaging. Int J Comput Appl. 2010;1:87–92. 21. Vijaya G, Vasudevan V. A novel noise reduction method using double bilateral filtering. Eur J Sci Res. 2010;46:331–8.