Noise reduction in dual‐energy computed tomography virtual monoenergetic imaging

Abstract Purpose Virtual monoenergetic images (VMIs) derived from dual‐energy computed tomography (DECT) have been explored for several clinical applications in recent years. However, VMIs at low and high keVs have high levels of noise. The aim of this study was to reduce image noise in VMIs by using a two‐step noise reduction technique. Methods VMI was first denoised using a modified highly constrained backprojection (HYPR) method. After the first‐step denoising, a general‐threshold filtering method was performed. Two sets of anthropomorphic phantoms were scanned with a clinical dual‐source DECT system. DECT data (80/140Sn kV) were reconstructed as VMI series at 12 different energy levels (range, 40‐150 keV, interval, 10 keV). For comparison, the averaged VMIs obtained from 10 repeated DECT scans were used as the reference standard. The signal‐to‐noise ratio (SNR), contrast‐to‐noise ratio (CNR) and root‐mean‐square error (RMSE) were used to evaluate the quality of VMIs. Results Compared to the original HYPR method, the proposed two‐step image denoising method could provide better performance in terms of SNR, CNR, and RMSE. In addition, the proposed method could achieve effective noise reduction while preserving edges and small structures, especially for low‐keV VMIs. Conclusion The proposed two‐step image denoising method is a feasible method for reducing noise in VMIs obtained from a clinical DECT scanner. The proposed method can also reduce edge blurring and the loss of intensity in small lesions.

feasibility of using iterative optimization algorithms to improve the image quality of DECT and resulting materials decomposition. 15,16 Consequently, the reconstruction of DECT-based VMIs can be improved. However, these advanced optimization methods are not provided by scanner vendors. Moreover, the raw data format is not explicitly described by scanner vendors, and image reconstruction requires calibration data. Lack of access to this data makes it difficult to implement the reconstruction of VMIs. One possible method to improve the image quality of VMIs is to apply an image denoising method directly on the DECT-derived VMIs. 14 One previous study showed that the highly constrained backprojection (HYPR) method 17,18 can be exploited to reduce noise in photon countingbased monoenergetic images. 13 In addition, HYPR has been used for reducing image noise in dynamic contrast-enhanced perfusion CT. 19,20 Although post-reconstruction denoising can improve the quality of monoenergetic images obtained from a preclinical photon counting-based spectral CT scanner, 13 it has not been validated using clinical DECT-derived VMIs. Moreover, reducing the radiation dose from DECT remains an important topic. 21 Using a low-dose DECT scan would increase the noise level which may affect the performance of HYPR. In order to further improve the image quality of DECT-based VMIs, we proposed a two-step noise reduction technique using a combination of HYPR 17,18 and the general-threshold filtering (GTF) method. 22 In this study, the proposed two-step noise reduction method was compared with the original HYPR method. 17,18 Two sets of anthropomorphic phantoms were used to assess the image quality and signal characteristics of denoised VMIs. We also investigated whether the studied image denoising methods could effectively reduce image noise while preserving edges and small structures.

2.A | Two-step noise reduction technique
In this study, we propose a two-step noise reduction technique to reduce image noise in DECT-derived VMIs by using a combination of HYPR 17,18 and GTF. 22 Firstly, VMIs obtained from vendor software were denoised using HYPR. 17,18 As originally developed for contrast-enhanced magnetic resonance angiography, 17 HYPR is a postprocessing technique that uses information obtained from all time-series images to improve the image quality of each individual time-series image. In brief, the HYPR-processed VMI (V HYPR ) at a virtual monochromatic energy level denoted by E is calculated as follows: where V(E) is the VMI at the energy level of E (keV) obtained from vendor software, CI is the composite image obtained from the sum of 12 V(E) (i.e. 40 to 150 keV in 10 keV intervals) and F is a box-kernel (low-pass) spatial filter function. 17 where WF nÂn V E ð Þ ð Þ denotes the adaptive Wiener filtering of V(E) with n × n window size. Note that the Wiener filter requires the noise variance to be set to the average of all the local estimated variances.
After the first-step processing, we observed that the modified HYPR reduced image noise only moderately. Thus, the HYPR-processed VMI obtained from Eq. (2) was refined by a second step. This second step used a GTF method originally developed for CT image reconstruction. 24 Our previous study demonstrates that the GTF method can be used for denoising diffusion weighted magnetic resonance imaging, 22 and it has good edge-preserving smoothing property. 22 In brief, GTF applied to V mHYPR (E) can be described as follows 22 : and , N i represents the 4-neighborhood of the i th pixel, λ is the regularization parameter that controls the filtering strength and p (= 0.9) is the norm of the regularization term.
Further details on the GTF method can be found in Refs. [22,24].
In this study, λ was set to the noise level of V mHYPR (E) obtained from the method described in Ref. [25]. The filtering process shown in Eq. (3) was repeated 40 times in order to obtain sufficient noise reduction.
Although GTF can remove noise while preserving edges, it leads to a certain loss of intensity in edges and small lesions. To address this problem, an additional step was performed to recover the intensity of edges and small lesions. First, we applied the Canny's edge detection algorithm to V GTF (E). Second, the edge (binary) image was dilated using a disk shaped structuring element with radius of 2 pixels. The dilated edge image may contain many pixels which had signal loss. Finally, the average of V GTF (E) and V mHYPR (E) was assigned to pixels belonging to the edges. Since V mHYPR (E) was less blurred than V GTF (E), the average of V GTF (E), and V mHYPR (E) can alleviate the loss of intensity while maintaining image quality. The final

2.C | Data analysis
In this study, averaged VMIs obtained from 10 repeated DECT where N denotes the total number of pixels in the image, V 1 E ð Þ is the CT number of the averaged VMI (i.e. 10 ND) in the i th pixel, and V F i E ð Þ is the CT number of the final denoised VMI obtained from one DECT scan (i.e. ND) in the i th pixel.  Fig. 3 show that the proposed method outperforms HYPR. Note that Fig. 3(a) shows the SNR of the tissue-equivalent solid material (see white square shown in Fig. 1). Figures 4-6 are the same as Figs. 1-3, respectively, but are obtained from a different axial slice. Similar findings can be observed. Note that Fig. 6(a) shows the CNR between the waterand tissue-equivalent solid materials (see white square shown in Fig. 4).

| RESULTS
To further evaluate the performance of the proposed method, a second phantom study was conducted. Figure 7 shows the DECT-derived VMIs of the anthropomorphic brain phantom for  Figure 8 shows the difference in VMIs between the 10 ND and the other three results (i.e. ND, ND + HYPR and ND + Proposed). Compared to HYPR, the proposed method has better edge-preserving performance, especially in low-keV VMIs. As shown in Fig. 9, the proposed method was superior to HYPR in terms of SNR and RMSE. However, we noticed that the improvement seems limited.
F I G . 5. Difference between the 10 normal-dose (ND) and the results of denoised ND (Fig. 4). From top to bottom: 40 keV; 60 keV; 90 keV; 120 keV; 150 keV. From left to right: 10 ND minus ND; 10 ND minus ND denoised by the highly constrained backprojection method; 10 ND minus ND denoised by the proposed method.
F I G . 6. The (a) contrast-to-noise ratio (CNR) and (b) root-mean-square error (RMSE) of various virtual monoenergetic images at different energy levels (40 to 150 keV). The CNR was calculated with two regions of interest (see white square shown in Fig. 4). The RMSE was calculated between the 10 normal-dose (ND) and the results of denoised ND.

| DISCUSSION
In this study, we propose a two-step noise reduction method for DECT-derived VMIs. We modified HYPR 17 F I G . 8. Difference between the 10 normal-dose (ND) and the results of denoised ND (Fig. 7). From top to bottom: 40 keV; 60 keV; 90 keV; 120 keV; 150 keV. From left to right: 10 ND minus ND; 10 ND minus ND denoised by the highly constrained backprojection method; 10 ND minus ND denoised by the proposed method.
F I G . 9. The (a) signal-to-noise ratio (SNR) and (b) root-mean-square error (RMSE) of various virtual monoenergetic images at different energy levels (40 to 150 keV). The SNR was calculated with a region of interest (see white square shown in Fig. 7). The RMSE was calculated between the 10 normal-dose (ND) and the results of denoised ND.  Fig. S1(d)]. Although the proposed noise reduction technique uses both the modified HYPR and GTF, these two methods can be used independently. We used the two-step approach because using either the modified HYPR or GTF provided limited improvement (data not shown).
Despite promising results obtained in this study, we note several issues in the present method. First, the results obtained from two anthropomorphic phantom studies may not be sufficient. Lowdose data and real patient data should be used to validate the performance of the proposed method. Second, in the case of the anthropomorphic brain phantom, the proposed method provided only moderate improvement. One possible reason is that the GTF method with 40 repetitions seems insufficient for the brain phantom (Figs. 7-9). The selection of optimal repetitions was not investigated, but will be studied in our future work. Third, we only compared the proposed method with the original HYPR. Other image denoising methods, including the time-intensity profile similarity bilateral filter, 27 the partial temporal nonlocal means filter, 28 and the k-means clustering guided bilateral filter, 29 can be used to reduce noise in VMIs. Because these methods have many parameters that need to be optimized, we did not implement these approaches in this study.
In this study, the modified HYPR used composite image obtained from the sum of 12 energy levels (i.e. 40 to 150 keV in 10 keV intervals). We found that the composite image obtained from the sum of six energy levels can provide similar results (data not shown).
In other words, increasing the number of energy levels may not improve the performance of the proposed method. One possible reason is that VMIs obtained from neighbouring energy levels have similar image statistical properties. As a result, the advantage of increasing the number of energy levels may be negligible. However, further improvements may be made in the following ways. First, the aforementioned methods [27][28][29]

CONF LICTS OF INTEREST
The authors have no relevant conflicts of interest to disclose.