Adaptive prior image constrained total generalized variation for low-dose dynamic cerebral perfusion CT reconstruction

Abstract

BACKGROUND:

Dynamic cerebral perfusion CT (DCPCT) can provide valuable insight into cerebral hemodynamics by visualizing changes in blood within the brain. However, the associated high radiation dose of the standard DCPCT scanning protocol has been a great concern for the patient and radiation physics. Minimizing the x-ray exposure to patients has been a major effort in the DCPCT examination. A simple and cost-effective approach to achieve low-dose DCPCT imaging is to lower the x-ray tube current in data acquisition. However, the image quality of low-dose DCPCT will be degraded because of the excessive quantum noise.

OBJECTIVE:

To obtain high-quality DCPCT images, we present a statistical iterative reconstruction (SIR) algorithm based on penalized weighted least squares (PWLS) using adaptive prior image constrained total generalized variation (APICTGV) regularization (PWLS-APICTGV).

METHODS:

APICTGV regularization uses the precontrast scanned high-quality CT image as an adaptive structural prior for low-dose PWLS reconstruction. Thus, the image quality of low-dose DCPCT is improved while essential features of targe image are well preserved. An alternating optimization algorithm is developed to solve the cost function of the PWLS-APICTGV reconstruction.

RESULTS:

PWLS-APICTGV algorithm was evaluated using a digital brain perfusion phantom and patient data. Compared to other competing algorithms, the PWLS-APICTGV algorithm shows better noise reduction and structural details preservation. Furthermore, the PWLS-APICTGV algorithm can generate more accurate cerebral blood flow (CBF) map than that of other reconstruction methods.

CONCLUSIONS:

PWLS-APICTGV algorithm can significantly suppress noise while preserving the important features of the reconstructed DCPCT image, thus achieving a great improvement in low-dose DCPCT imaging.

Keywords

DCPCT reconstruction PWLS total generalized variation prior image

1 Introduction

Acute stroke is one of the leading threats for human life with high rates of mortality, disability, and recurrence [1 , 36]. Dynamic cerebral perfusion CT (DCPCT) has been widely used to assess the hemodynamic status of the brain by generating functional maps of cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT) [5 , 50]. DCPCT is performed with the acquisition of sequential CT images in cine mode after the intravenous injection of iodinated contrast. However, repeated multiple CT scans result in excessive radiation exposure to patients [15 , 41], which has raised great concerns on the safety of DCPCT examination.

Reducing the current of x-ray tube in data acquisition is a straightforward approach to perform low-dose DCPCT imaging. However, this leads to a decrease in the number of detected photons, increasing quantum noise in the projection data. Thus, DCPCT sequence images reconstructed using the standard filtered back-projection (FBP) algorithm exhibit strong artifacts and noise. Extracting accurate perfusion information from sequence images with excessive noise remains a challenge [2 , 45]. To obtain high-quality images under low-dose conditions, several strategies have been proposed. An essential strategy is the statistical iterative reconstruction (SIR) technique for low-dose DCPCT. The SIR method models the system imaging process and the statistical characteristics of the measured sinogram data [37, 39]. The cost function of the SIR typically includes two parts: the first part includes the statistical properties of the measured sinogram data, and the second part is regularization term. Penalized weighted least squares (PWLS) is a commonly used cost function in SIR [27 , 38]. The regularization in PWLS criterion is critical for low-dose DCPCT image reconstruction. The regularization term incorporates the prior information of the target image into the cost function as a penalty term to constrain the solution space and ensure more reliable and stable results [28, 31].

In the last decade, various regularizations have been developed for the PWLS method in DCPCT image reconstruction. Leveraging the structural correlations between the diverse frames, Zeng et al. treated DCPCT sequence images as a composition of low-rank, sparse, and noise components, and subsequently introduced a tensor-based sparse regularization approach for low-dose DCPCT reconstruction [45]. Taking into account the global spatial-temporal correlation of the sequence images, Li et al. proposed a spatial-temporal total variation and regularization of low-rank tensor decomposition for low-dose DCPCT reconstruction [18]. DCPCT imaging typically involves a series of scans of the same anatomical brain region; substantial structural similarities exist between high-quality images acquired during pre-contrast scans and the DCPCT sequence images. Recently, there has been increased interest in incorporating these high-quality images as prior information into regularization. Ma et al. introduced an SIR method that relies on an edge preservation technique induced by a normal dose pre-contrast scanned CT image [19]. This method utilizes the nonlocal mean to construct a reference image for the regularization of the target image, effectively reducing the reliance on a highly accurate image registration algorithm; however, this approach can result in excessive spatial over-smoothing, impacting imaging quality. Niu et al. proposed a diffusion tensor based regularization for low-dose DCPCT image reconstruction [29]. The primary objective of this approach was to decrease the reconstruction error caused by the difference between the high-quality prior image and target image; however, complicated parameter configurations produced significant limitations in practical applicability. Lauzier et al. formulated a statistical regularization known as prior image constrained compressed sensing to improve the quality of low-dose DCPCT reconstruction [17]. This was achieved by minimizing the total variation between the target image and the high-quality prior image. However, a limitation of this algorithm is that it assumes that there is no significant deformation between the target image and the prior image, which may not be true in many clinical scenarios.

To mitigate the challenges of matching the target image and the high-quality prior image, we developed an adaptive prior image constrained total generalized variation (APICTGV) regularization for low-dose DCPCT PWLS reconstruction. The presented reconstruction algorithm is known as PWLS-APICTGV. Furthermore, an alternating minimization algorithm is developed to solve the cost function of the PWLS-APICTGV reconstruction. The presented PWLS-APICTGV algorithm has two advantages. First, it can adaptively select appropriate matching weights to accurately integrate the structural information from the prior image into the low-dose DCPCT reconstruction. The weights were calculated by the normalized eigenvectors of the target image and the prior image, and the weights can identify the difference between these two images. Second, it can maintain the structural features of the target image when the noise level of the reconstructed image is high. The results of experiment using both digital brain perfusion phantom and patient data show that the presented PWLS-APICTGV method can successfully exploit the supplementary structure information from the prior image to suppress the noise in the target image while preserving intrinsic features.

2 Methods and materials

2.1 PWLS image reconstruction

For each time frame of the DCPCT sequence images, the statistical properties of noise in the measured sinogram data can be formulated as an independent Gaussian distribution [20, 39]; its variance can be calculated as follows: $σ_{ki}^{2} = \frac{1}{I_{0}} exp ({\bar{y}}_{ki}) (1 + \frac{1}{I_{0}} exp ({\bar{y}}_{ki}) (σ_{e}^{2} - 1.25))$ (1) where $σ_{ki}^{2}$ and ${\bar{y}}_{ki}$ represent the variance and mean of the projected data, respectively, at the detector i and time frame k. I₀ denotes the count of incident photons and $σ_{e}^{2}$ represents the variance of the electronic noise. With the above-mentioned noise variance of the projection data, the PWLS reconstruction can be written as follows: $min_{μ_{k} ⩾ 0} (y_{k} - H μ_{k})^{T} Σ^{- 1} (y_{k} - H μ_{k}) + β R (μ_{k})$ (2) where y_k and μ_k are the projection data and the desired DCPCT image at time frame k, respectively. The operator H is the DCPCT imaging system matrix, and T denotes the transpose operation. Σ is the diagonal weighting matrix with the i - th element of $σ_{ki}^{2}$ , calculated using Equation (1). R (μ_k) represents the regularization, and β > 0 is a penalty parameter that controls the trade-off between the measured and estimated projection data.

2.2 Prior image constrained total generalized variation

The second-order total generalized variation (TGV) is formulated as follows [3]: ${TGV}_{α}^{2} (u) = min_{w \in Ω} α_{1} | | \nabla u - w | |_{1} + α_{2} | | ɛ (w) | |_{1}$ (3) where Ω is an open subset of Rⁿ with a Lipschitz continuous boundary and w is a vector in Ω. The linear operator ∇ represents the discrete gradient operator and ɛ represents the symmetrized derivative operator. The symmetrized derivative operator is defined as $ɛ (w) = \frac{1}{2} (\nabla w + \nabla w^{T})$ . Incorporating the high-quality prior image μ_p into the TGV, the prior image constrained TGV (PICTGV) is formulated as follows [26]: $λ {TGV}_{α}^{2} (μ_{k} - μ_{p}) + (1 - λ) {TGV}_{α}^{2} (μ_{k})$ (4) where λ ∈ [0, 1] is a weight that determines the trade-off between the two TGV terms in equation (4). Supplemental structure information from the high-quality prior image μ_p is incorporated into the reconstructed image μ_k by the subtraction operation μ_k - μ_p. To mitigate the difference between the prior image μ_p and the target image μ_k, ${TGV}_{α}^{2} (μ_{k})$ was integrated into the PICTGV with a weight of 1 - λ.

2.3 Adaptive prior image constrained total generalized variation

The weight determines the conformity between the prior image and the target image. If the prior image has an excessive impact on the target image, it can inadvertently result in the loss of essential perfusion details as the prior image inherently lacks perfusion-specific information. On the other hand, a small λ will cause the target image to have an excessive influence on the reconstruction process, the result will contain a lot of noise because the supplementary structural information from the prior image is not fully exploited.

In this study, we used the orientation information derived from the structure tensors of the high-quality prior images μ_p and the target image μ_k to calculate the weight value λ in PICTGV regularization. Let ST (μ_k) and ST (μ_p) be the structure tensor of the images μ_p and μ_k, respectively. The adaptive weight λ_{μ
_k} can be formulated as follows: $λ_{μ_{k}} = sin (abs (arccos (v (μ_{p}) \cdot v (μ_{k})) - \frac{π}{2}))$ (5) where abs (·) denotes the absolute value function, v (μ_p) and v (μ_k) represent the normalized eigenvectors of the structure tensor ST (μ_k) and ST (μ_p), respectively. Incorporating the adaptive weight λ_{μ
_k} into the PICTGV regularization, the APICTGV regularization can be formulated as follows: $λ_{μ_{k}} {TGV}_{α}^{2} (μ_{k} - μ_{p}) + (1 - λ_{μ_{k}}) {TGV}_{α}^{2} (μ_{k})$ (6) where λ_{μ
_k} can be calculated by equation (5).

2.4 PWLS-APICTGV image reconstruction algorithm

Based on APICTGV regularization, the PWLS-APICTGV reconstruction can be written as $min_{μ_{k} ⩾ 0} (y_{k} - H μ_{k})^{T} Σ^{- 1} (y_{k} - H μ_{k}) + β (λ_{μ_{k}} {TGV}_{α}^{2} (μ_{k} - μ_{p}) + (1 - λ_{μ_{k}}) {TGV}_{α}^{2} (μ_{k}))$ (7)

The equation (7) can be solved by an alternating minimization algorithm with two steps: $μ_{k}^{n + 1 / 2} = \underset{μ_{k} ⩾ 0}{arg min} (y_{k} - H μ_{k})^{T} Σ^{- 1} (y_{k} - H μ_{k})$ (8) $μ_{k}^{n + 1} = \underset{μ_{k}}{arg min} \frac{1}{2} | | μ_{k} - μ_{k}^{n + 1 / 2} | |_{2}^{2} + \frac{β}{η} (λ_{μ_{k}} {TGV}_{α}^{2} (μ_{k} - μ_{p}) + (1 - λ_{μ_{k}}) {TGV}_{α}^{2} (μ_{k}))$ (9) where n is the index for the iteration steps and || · ||₂ represents the Euclid norm. Equation (8) is solved using the gradient descent algorithm, which can be expressed as: $μ_{k}^{n + 1 / 2} = μ_{k}^{n} - η H^{T} Σ^{- 1} (H μ_{k}^{n} - y_{k})$ (10) where η > 0 is the step size that is calculated by the following formula: $η = \frac{| | H^{T} Σ^{- 1} (H μ_{k}^{n} - y_{k}) | |_{2}^{2}}{| | Σ^{- 1 / 2} {HH}^{T} Σ^{- 1} (H μ_{k}^{n} - y_{k}) | |_{2}^{2}}$ (11)

The problem in equation (9) can be decomposed into the following two sub-problems by the composite splitting approach [6]: $μ_{k 1}^{n + 1} = arg min_{μ_{k}} \frac{η}{2} | | μ_{k} - μ_{k}^{n + 1 / 2} | |_{2}^{2} + \frac{(1 - λ_{μ_{k}}) β}{m_{1}} {TGV}_{α}^{2} (μ_{k})$ (12) $μ_{k 2}^{n + 1} = arg min_{μ_{k}} \frac{η}{2} | | μ_{k} - μ_{k}^{n + 1 / 2} | |_{2}^{2} + \frac{λ_{μ_{k}} β}{m_{2}} {TGV}_{α}^{2} (μ_{k} - μ_{p})$ (13) $μ_{k}^{n + 1} = \frac{μ_{k, 1}^{n + 1} + μ_{k, 2}^{n + 1}}{2}$ (14) where m₁ and m₂ are two positive-valued scalars, which satisfy m₁ + m₂ = 1. In this study, we set m₁ = m₂ = 0.5 for all dataset. The sub-problems in equations (12) and (13) can be solved by the prime-dual algorithm described in [16, 24].

The PWLS-APICTGV reconstruction can be implemented as follows:

Step 1. Update $μ_{k}^{n + 1 / 2}$ using the formula in equation (10) with initial value $μ_{k}^{0}$ .

Step 2. Update λ_{μ
_k} using equation (5) with the intermediate image $μ_{k}^{n + 1 / 2}$ and the prior image μ_p.

Step 3. Update $μ_{k}^{n + 1}$ according to equations (12), (13) and (14).

Step 4. Repeat steps 1– 3 until the stop criterion is met. Repeat steps 1– 4 to reconstruct DCPCT sequence images. The initial value $μ_{k}^{0}$ was set to the FBP image.

2.5 Selection of parameters

2.5.1 Selection of β

The parameter β balances the trade-off between data fidelity and regularization terms. Finding an optimal β is still an open problem in model-based iterative CT reconstruction [11, 33]. In this work, β was determined using a trial and error strategy and visual inspection to achieve the best image quality. In studies of digital phantom and patient data, the parameter β was set to be 5.0 × 10^-2 and 3.0 × 10^-2, respectively.

2.5.2 Selection of stop criterion

Relative error (RE) was used as the stop criterion in the PWLS-APICTGV algorithm. The RE is formulated as: $RE = \frac{| | μ_{k}^{n + 1} - μ_{k}^{n} | |_{2}}{| | μ_{k}^{n} | |_{2}} .$ (15) RE describes the difference between two successive iterations. The PWLS-APICTGV algorithm is stopped when RE ⩽ 1 ×10^-3 or the maximum number of iterations reaches 50.

2.6 Data acquisition

2.6.1 Digital phantom

Low-dose DCPCT data are simulated using a realistic digital brain perfusion phantom [21]. The DCPCT projection data can be obtained using the simulation method in [19, 25] by setting the incident x-ray intensity to be 5.0 × 10⁴. The imaging parameters of the CT scanner were described as follows: (1) the distances from the x-ray tube to the rotation center is 541 mm; (2) the distance from the rotation center to the detector array is 408 mm; (3) 984 projection views are evenly spanned on a circle orbit in each rotation; (4) the number of channels for each projection view is 888. The low-dose DCPCT image is reconstructed using the FBP algorithm. The image is of 256 × 256array, and the pixel size is 2 mm×2 mm.

2.6.2 Patient data

The DCPCT sequence image of a patient was acquired using a GE CT scanner. Initially, an unenhanced scan was conducted on a patient at 120 kVp and 400 mA. Then, iodinated contrast (40– 50 ml) was injected at a rate of 5 ml/s. Cine-enhanced scan was performed at 80 kVp and 300 mA. To prevent the need for another scan of the patient, normal-dose DCPCT images serve as the ground truth to simulate low-dose DCPCT projection using the approach described in Section 2.6.1. The low-dose DCPCT sequence image is reconstructed using the FBP algorithm. The image is of 512 × 512 array, and the pixel size is 1 mm×1 mm.

2.7 Performance evaluation

2.7.1 Reconstruction accuracy

Relative root mean square error (RRMSE) is used to evaluate the reconstruction accuracy of different algorithms. The RRMSE is written as follows: $RRMSE = \sqrt{\frac{\sum_{s} (μ (s) - μ_{ref} (s))^{2}}{\sum_{s} (μ_{ref} (s))^{2}}}$ (16) where μ (s) and μ_ref (s) denote the values of the test image and the reference image in pixel s, respectively.

2.7.2 Image similarity indexes

The feature similarity (FSIM) index [48] and the structural similarity (SSIM) index [40] are used for reconstruction quality evaluation. The FSIM and SSIM indexes rage from 0 to 1. A higher FSIM index implies a stronger similarity in features between the test image and the reference image, while a higher SSIM index suggests a superior similarity in structure details between the test image and the reference image.

2.7.3 Hemodynamic parameter map

According to the perfusion theory model in [30], the concentration time curve C (t) can be calculated as follows: $C (t) = CBF \cdot (C_{a} (t) \otimes F (t))$ (17) where C_a (t) is the arterial input function, F (t) represents the residue function, and the symbol ⊗ denotes the convolution operator. CBF · F (t) can be obtained using the truncated singular value decomposition (TSVD) deconvolution algorithm [9]. Then the hemodynamic parameter map CBF can be obtained by max(CBF · F (t)).

2.7.4 Comparison methods

To evaluate the performance of the PWLS-APICTGV reconstruction algorithm, we use the FBP reconstruction algorithm, the PWLS-ndiNLM reconstruction algorithm [19], the PWLS-PIDT reconstruction algorithm [29], the vox-level TAC correction (VTC) algorithm [5], and the PICTGV based PWLS (PWLS-PICTVG) reconstruction algorithm for comparison. Notice that the PWLS-APICTGV algorithm will reduce to the PWLS-PICTGV algorithm when the weight is set to a constant.

3 Results

3.1 Digital brain perfusion phantom study

3.1.1 Reconstruction results

The reconstructed DCPCT images of the digital phantom are depicted in Fig. 2. Rows 1– 4 rows correspond to time frames 5, 15, 25, and 35, respectively. The first column is the phantom, serving as a reference for image quality evaluation. The second column shows the images reconstructed using the FBP algorithm. It is evident that the quality of the FBP image is severely degraded due to the low-dose x-ray incident intensity. Columns 3– 6 show the DCPCT images reconstructed using the PWLS-ndiNLM, PWLS-PICTGV, PWLS-PIDT, and VTC algorithms, respectively. Although these images exhibit some degree of noise reduction compared to FBP images, some undesirable noise is still observable. Column 7 is the DCPCT images reconstructed by the PWLS-APICTGV algorithm. Noise is greatly reduced and fine structure and edges are also preserved.

Fig. 1

The digital brain perfusion phantom.

Fig. 2

The DCPCT images of digital phantom correspond to time frames 5, 15, 25, and 35, respectively. The display window is [10 60] HU.

3.1.2 Reconstruction accuracy

To quantitatively assess the performance of the various reconstruction algorithms, we calculated the RRMSE of the DCPCT sequence image. Figure 3 shows the RRMSE curves of different algorithms. The mean RRMSE of the DCPCT sequence image reconstructed using the PWLS-ndiNLM, PWLS-PICTGV, PWLS-PIDT, and VTC algorithms are 0.0519, 0.0323, 0.0344, and 0.0484, respectively. The average RRMSE of the DCPCT sequence image reconstructed by the PWLS-APICTGV algorithm reduces to 0.0226. These results indicate that PWLS-APICTGV algorithm achieves the best performance in terms of reconstruction accuracy.

Fig. 3

RRMSE curves of the different reconstruction algorithms for digital brain perfusion phantom.

3.1.3 Structural similarity study

To further show the difference between the reconstructed results, a zoomed region of interest (ROI) from the images in Fig. 2 is depicted in Fig. 4. This ROI contains an infarct core and an ischemic penumbra. It is evident that the quality of FBP image is severely degraded, the infarct core and ischemic penumbra can be hardly distinguished from the noise. Although the noise was suppressed in the results reconstructed using the PWLS-ndiNLM, PWLS-PICTGV, PWLS-PIDT, and VTC algorithm, some undesirable noise still exists in the region around the infarct core and the ischemic penumbra. In the images reconstructed by the presented PLWS-APICTGV algorithm, the noise is greatly reduced, and the fine structure and edge are preserved. Figure 5 shows the SSIM curves of the ROI. The mean SSIM of the PWLS-ndiNLM, PWLS-PICTGV, PWLS-PIDT, and VTC sequence image are 0.9487, 0.9818, 0.9777, and 0.9914, respectively. The mean SSIM of the PWLS-APICTGV sequence image increases to 0.9973.

Fig. 4

Zoomed-in view of the ROI in Fig. 2. The display window is [10 60] HU.

Fig. 5

SSIM curves of the different reconstruction algorithms for digital brain perfusion phantom.

3.1.4 Cerebral hemodynamic parameters

Figure 6 shows the CBF maps derived from the DCPCT sequence images reconstructed using different algorithms. The CBF obtained from the digital phantom serves as a reference for quantitative image quality assessment. The CBF map derived from low-dose FBP images exhibits severe noise, rendering it inadequate for clinical diagnosis. Although the noise in the CBF maps derived from PWLS-ndiNLM, PWLS-PICTGV, PWLS-PIDT, and VTC sequence images is efficiently reduced, some residual noise can still be observed. It is evident that the PWLS-APICTGV algorithm achieves the best CBF map that matches the ground truth. To quantitatively evaluate the image quality of these CBF, SSIM and FSIM indexes of each CBP map are depicted in Table 1. The CBP map obtained from the PWLS-APICTGV sequence images has the highest SSIM and FSIM compared to other reconstruction algorithms.

Fig. 6

CBF maps obtained from DCPCT sequence images for digital brain perfusion phantom.

Table 1

SSIM and FSIM indexes of the CBF maps for digital brain perfusion phantom

	FBP	PWLS-ndiNLM	PWLS-PICTGV	PWLS-PIDT	VTC	PWLS-APICTGV
FSIM	0.8007	0.9676	0.9728	0.9697	0.9226	0.9776
SSIM	0.4896	0.8881	0.9034	0.8905	0.7894	0.9305

3.2 Patient data study

3.2.1 Reconstructed images

Figure 7 shows the reconstructed DCPCT image of patient data. The rows represent different time frames, namely 5, 15, 25, and 35. The first column displays the normal-dose DCPCT image, which serves as the ground truth for image quality evaluation. The low-dose DCPCT images reconstructed by the FBP algorithm, in the second column, exhibit severely degraded image quality. The third to fifth columns display the DCPCT image reconstructed using the PWLS-ndiNLM, PWLS-PICTGV and PWLS-PIDT algorithms, respectively, which successfully reduce the noise compared to FBP images. However, some undesired noise remains visible. The sixth column is the DCPCT images reconstructed using the PWLS-APICTGV algorithm, whose noise level is lower than that of the DCPCT images reconstructed by other competing algorithms.

Fig. 7

DCPCT images of the patient data correspond to time frames 5, 15, 25, and 35. The display window is [368, 526] HU.

3.2.2 Reconstructed accuracy

Figure 8 shows the RRMSE curves of the different reconstruction algorithm for patient data. The mean RRMSE of the DCPCT sequence image reconstructed using the PWLS-ndiNLM, PWLS-PICTGV and PWLS-PIDT algorithms are 0.0346, 0.0242, and 0.0243, respectively. The mean RRMSE of the DCPCT sequence image reconstructed using the PWLS-APICTGV algorithm reduces to 0.0173.

Fig. 8

RRMSE curves of the different reconstruction algorithms for patient data.

3.2.3 Structural similarity

Figure 9 shows a zoomed ROI of the images in Fig. 7. The SSIM curves of ROI in Fig. 9 are shown in Fig. 10. The mean SSIM of the FBP sequence image is 0.4128. The mean SSIM of the PWLS-ndiNLM, PWLS-PICTGV, and PWLS-PIDT sequence image are 0.7190, 0.7563, and 0.7705, respectively. The mean SSIM of the PWLS-APICTGV sequence image increases to 0.8127.

Fig. 9

Zoomed-in views of the ROI in Fig. 7. The display window is [368, 526] HU.

Fig. 10

SSIM curves of different reconstruction algorithms for patient data.

3.2.4 Cerebral hemodynamic parameters

Figure 11 shows the CBF maps of the patient data. The quality of CBF map generated from FBP sequence image is severely degraded. The CBF maps obtained from the PWLS-ndiNLM, PWLS-PICTGV, and PWLS-PIDT sequence image demonstrate a remarkable noise suppression when compared to the FBP algorithm. However, some residual noise is still visible in these maps. The CBF map derived from PWLS-APICTGV sequence images exhibits the best quality, which achieves the best matching for the normal-dose CBF map. Table 2 shows the FSIM and SSIM of the CBF maps. It is evident that the PWLS-APICTGV algorithm has the highest FSIM and SSIM compared to other competing reconstruction algorithms.

Fig. 11

CBF maps of the patient data.

Table 2

FSIM and SSIM values of CBF maps in Fig. 11

	FBP	PWLS-ndiNLM	PWLS-PICTGV	PWLS-PIDT	PWLS-APICTGV
FSIM	0.7652	0.8230	0.8261	0.8686	0.9070
SSIM	0.4656	0.7735	0.7785	0.8195	0.8566

4 Discussion and conclusion

In this paper, we present an iterative PWLS-APICTGV reconstruction algorithm to improve the image quality of low-dose DCPCT using the adaptive structure information from a high-quality precontrast CT image. Supplemental information from a high-quality precontrast CT image is incorporated into DCPCT reconstruction using an adaptive structure prior that can identify the difference between the target image and the prior image. The PWLS-APICTGV algorithm can detect the anatomical structure in the target image that matches the high-quality prior image, resulting in improved noise suppression and edge preservation as indicated by the digital phantom and patient data studies.

In our digital phantom study, the experiment results show that the PWLS-APICTGV algorithm achieves the best performance compared to other competing algorithms in terms of noise reduction and edge preservation. The PWLS-APICTGV algorithm can produce adequate DCPCT images and CBF map as demonstrated in Figs. 2 and 6. It can be seen that not only is the noise significantly suppressed, but fine details and edges are also accurately preserved. RRMSE, FSIM, and SSIM studies further show the quantitative gains of the presented PWLS-APICTGV algorithm. To further evaluate performance of the PLWS-APICTG algorithm at different exposure levels, we simulated a range of dose levels by setting the incident photons to be 1.0 × 10⁴, 2.5 × 10⁴, 7.5 × 10⁴ and 1.0 × 10⁵. The FBP images of these four different dose levels are shown in Fig. 12. For FBP algorithm, when the dose level is decreased, more noise appears in the FBP image as anticipated from CT imaging physics. In contrast, in the PWLS-APICTGV reconstructions, displayed in Fig. 13, the noise is greatly reduced at all dose levels. The average RRMSE and SSIM values is calculated at different dose levels, the results are depicted in Fig. 14. This results indicated that PLWS-APICTGV algorithm can achieve high reconstruction accuracy at different low dose levels. In patient data study, normal-dose DCPCT sequence image is used as the ground truth to assess the performance of different algorithms. The structure similarity study shows the superiority of the presented PWLS-APICTGV algorithm in terms of noise reduction and edge preservation. Moreover, the PWLS-APICTGV algorithm can generate the best matching CBF map with those obtained from normal-dose DCPCT sequence images, as indicated by Fig. 11 and Table 2. Notice that the results of the PWLS-APICTGV algorithm reach a conclusion that is consistent with that of the digital phantom study.

Fig. 12

FBP image at different dose levels with four representative time frames.

Fig. 13

Reconstructions of PWLS-APICTGV algorithm at different dose levels with four representative time frames.

Fig. 14

The average RRMSE and SSIM values of DCPCT images reconstructed by PWLS-APICTGV algorithm at different dose levels.

Although the performance of the PWLS-APICTGV reconstruction algorithm is promising, there are still some unresolved problems in its current form. The first question is how to find an optimal penalty parameter β. The value of β is highly related to the smoothness of the reconstructed DCPCT sequence images. A higher penalty value will yield oversmoothed results, while a lower one will result in noisy results. In practical implementation, we initially assigned a high value to β, then gradually lower its value until we obtain desired DCPCT images. This strategy is regarded as a trial and error procedure. Developing an automatic method to determine the adequate penalty parameter will be an interesting topic for future research. Another problem is the computation time of the PWLS-APICTG reconstruction. The repeated forward and back projection operators greatly increase the computation time of the PWLS-APICTGV image reconstruction, which will be a challenge for its practical use. However, the PWLS-APICTGV algorithm can be sped up using graphics processing unit (GPU) and parallel computation [13, 44]. Lastly, the CBF map is calculated using the TSVD deconvolution algorithm, which would lead to some unsatisfactory oscillations and an overestimation of the CBF [7]. This shortcoming has prompted studies that impose various regularizations on the DCPCT sequence images to enhance the stability of CBF estimation [8 , 49]. Incorporating APICTGV regularization on the DCPCT images into the CBF estimation will be an interesting topic in future study.

In recent years, deep learning-based image prior have been applied to low-dose cerebral perfusion CT image reconstruction [10 , 46]. Deep learning techniques, with the advanced deep network structure and large-scale data-driven training processes, demonstrate exceptional capabilities in image feature extraction. Integrating the deep learning technique in DCPCT image reconstruction will effectively capture and extract the subtle features from the sequential images, which can generate a corresponding prior image with minimum error compared to the target image. Embedding the deep learning techniques in to TGV regularization will be an interesting topic for future research.

In summary, we present an iterative PWLS-APICTGV algorithm to improve the image quality of low-dose DCPCT reconstruction. The PWLS-APICTGV method can adaptively implant the edge and structure information from the prior image into low-dose DCPCT reconstruction. PWLS-APICTGV algorithm can significantly suppress noise while preserving the important features of the reconstructed DCPCT image, thus achieving a great improvement in low-dose DCPCT imaging. Consequently, the presented PWLS-APICTGV algorithm shows great potential for reducing radiation exposure and may be applied to clinical settings in the future.

Footnotes

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (62261002, 11701097, 81827804, U21A6005, 12226004), Science and Technology Program of Jiangxi Province (20192BCB23019, 20202BBE53024), Jiangxi Double Thousand Plan (jxsq2019201061).

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