Robust low-dose dynamic cerebral perfusion CT image restoration via coupled dictionary learning scheme

Abstract

Dynamic cerebral perfusion x-ray computed tomography (PCT) imaging has been advocated to quantitatively and qualitatively assess hemodynamic parameters in the diagnosis of acute stroke or chronic cerebrovascular diseases. However, the associated radiation dose is a significant concern to patients due to its dynamic scan protocol. To address this issue, in this paper we propose an image restoration method by utilizing coupled dictionary learning (CDL) scheme to yield clinically acceptable PCT images with low-dose data acquisition. Specifically, in the present CDL scheme, the 2D background information from the average of the baseline time frames of low-dose unenhanced CT images and the 3D enhancement information from normal-dose sequential cerebral PCT images are exploited to train the dictionary atoms respectively. After getting the two trained dictionaries, we couple them to represent the desired PCT images as spatio-temporal prior in objective function construction. Finally, the low-dose dynamic cerebral PCT images are restored by using a general DL image processing. To get a robust solution, the objective function is solved by using a modified dictionary learning based image restoration algorithm. The experimental results on clinical data show that the present method can yield more accurate kinetic enhanced details and diagnostic hemodynamic parameter maps than the state-of-the-art methods.

Keywords

Low-dose dynamic cerebral perfusion computed tomography dictionary learning image restoration

1 Introduction

Dynamic cerebral perfusion x-ray computed tomography (PCT) has been advocated for the diagnosis of acute ischemic stroke or chronic cerebrovascular diseases using hemodynamic parameters in recent years [1 –5]. Usually, the hemodynamic parameters are calculated for each tissue voxel independently from the obtained PCT image serials via singular value decomposition (SVD) method or its variants [6]. In practice, to produce robust hemodynamic parameters, accurate time density curve (TDC) and arterial input function (AIF) are needed by setting a repeated normal-dose scan protocol, which can significantly increase radiation exposure to patients. Therefore, it is anticipated that PCT imaging will be substantially curtailed unless radiation dose is reduced [7 –10].

To address the abovementioned radiation dose issue of PCT imaging, many studies have been reported to improve the PCT images quality or hemodynamic parameters estimation accuracy with a low-dose scan protocol including low-milliampere-seconds (low-mAs), low-kilovoltage-peak (low-kVp), sparse-view and so on [11 –24]. Among them, one typical category is to apply image post-processing on the filtered back projection (FBP) reconstructed PCT images directly to suppress noise-induced artifacts effectively [12 –14]. For example, Mendrik et al. proposed a time-intensity profile similarity bilateral filtering method to reduce the PCT image noise [12]. Supanich et al. introduced a highly constrained back projection (HYPR) method by using a time-averaged and low-noise composite image as a base to acquire high-quality PCT images [13]. To utilize the redundancy information in the previous normal-dose PCT scan, Ma et al. developed a previous normal-dose unenhanced scan induced nonlocal means (ndiNLM) method for low-dose PCT images restoration [14]. Ma et al. further extended the ndiNLM concept into sequential PCT image iterative reconstruction for accurate TDC estimation by designing a previous normal-dose unenhanced scan induced regularization [17]. Instead of improving the PCT images quality, another category is to estimate hemodynamic parameters directly with an iterative deconvolution fashion [20 –23]. For example, He et al. developed a four-dimension spatio-temporal deconvolution method without distinguishing the spatial and temporal components, only regularizing the homogeneous four-dimension regions and edge-field differently [20]. Fang et al. further proposed a robust tensor total-variation (TTV) regularization involving the temporal and spatial correlation information in the deconvolution model [23].

Recently, the approach of sparsifying images using a redundant dictionary, known as dictionary learning (DL), has been widely used in the CT field [25 –34]. Compared to pixel-wise intensity update-based restoration methods, DL-based methods process the objective image patch by patch [35, 36]. Specifically, a dictionary is a collection of atoms learned from application-specific training images. Then, the objective image is divided into many overlapped patches, represented sparsely by over-completed elements of the learned dictionary. Since the dictionary is learned from the patches of the training images and tends to effectively capture local image features as well as structural similarities, the DL-based methods enable a more effective representation of patch-shaped features in objective images to other generic sparse transform-based methods, leading to a superior image recovery [35 –39].

Given the aforementioned advantages, in this study, we developed an image restoration method by utilizing coupled dictionary learning (CDL) scheme to yield a clinically acceptable cerebral PCT image with low-mAs. This CDL scheme divided the dynamic PCT images into two parts: the background part and the enhancement part. The background part is selected as the average of baseline time frames, i.e., the first ten frames. And the enhancement part is the subtraction between the enhanced time frames and the background part. Then two dictionaries are trained based on the 2D background information and 3D enhancement information with spatio-temporal patches of enhanced regions. Then the low-dose PCT images are restored by using the general DL processing. Specially, the 3D enhancement information is acquired from normal-dose cerebral PCT images considering the low noise level. To summarize, the main contribution of the work is as follows: (1) we present a CDL-based framework which learns a pair of dictionaries, i.e., background dictionary and enhanced dictionary, simultaneously from the 2D background information and 3D enhanced information for PCT images restoration; (2) we propose a modified dictionary learning based image restoration algorithm to obtain a robust solution. The experimental results show that the present CDL method outperforms state-of-the-art DL-based methods not only in obtaining good noise-resolution tradeoff, but also in yielding accurate kinetic enhanced details, leading to visually more pleasant diagnostic hemodynamic parameter maps (HPM) outputs.

The remaining part of this paper is organized as follows. Section 2 reviews the DL based model and then describes the present CDL scheme, and the associative optimization approach. The experimental setup and evaluation metrics are also presented in this section. In Section 3, the experimental results are reported. The discussion and conclusion are given in Section 4.

2 Methods and materials

2.1 Brief review of DL model

In 2006, Elad et al. presented a successful application of the DL method in image restoration [35]. In the DL method, a vector y ∈ R^M×1 denotes a noisy image of H × W pixels and a vector x ∈ R^M×1 denotes its corresponding desired image wherein M = H × W. A set of small overlapping patches with the size of $\sqrt{N} \times \sqrt{N}$ can be extracted from the image. With the sliding distance of the patch window setting as one pixel, we will have $(H - \sqrt{N} + 1) \times (W - \sqrt{N} + 1)$ patches. Mathematically, the DL-based image restoration algorithm can be formulated as follows: $min_{x, D, α} {∥ x - y ∥}_{2}^{2} + λ_{s} \sum_{s} ({∥ R_{s} x - D α_{s} ∥}_{2}^{2} + γ_{s} {∥ α_{s} ∥}_{0})$ (1) where R_s ∈ R^N×M represents an operator that extracts a patch x_s of $\sqrt{N} \times \sqrt{N}$ pixels from desired image x, and s denotes the image patch index. The regularization parameter λ_s is related to the noise level of image y. The parameter γ_s is the Lagrange multiplier. The dictionary D ∈ R^N×K is a matrix composed of K atoms. And the vector α_s ∈ R^K×1 denotes the coefficient for the sparse representations of patch x_s with respect to the dictionary D. The l₀-norm ∥α_s ∥ ₀ counts the non-zero entries of the vector α_s and can be replaced by the l₁-norm to make it easier to solve [40].

Based on [35], the minimization problem in (1) is equivalent to solve the following two optimization problems: $min_{D, α} \sum_{s} {∥ α_{s} ∥}_{0} s . t . {∥ R_{s} x - D α_{s} ∥}_{2}^{2} \leq ɛ, \forall s$ (2) $min_{x} {∥ x - y ∥}_{2}^{2} + λ_{s} \sum_{s} {∥ R_{s} x - D α_{s} ∥}_{2}^{2}$ (3) where the parameter ɛ denotes the tolerance used for calculating α by the orthogonal matching pursuit (OMP) algorithm and is modulated with respect to the level of image noise. Minimization problem in Equation (2) aims to train the dictionary D and coefficients α from a set of image patches and can be solved by the classical K-means Singular Value Decomposition (K-SVD) method [36]. Then, with the fixed D and α, the desired image x can be obtained by solving Equation (3) through zeroing the first order derivative of Equation (3) with respect to image x: $x = {(I + λ_{s} \sum_{s} R_{s}^{T} R_{s})}^{- 1} (y + λ_{s} \sum_{s} R_{s}^{T} D α_{s})$ (4) where I is the identity matrix.

2.2 Overview of CDL scheme

The proposed CDL scheme exploits the rich redundancy and similarity information within both the low-dose PCT image sequence and normal-dose PCT image sequence to restore the low-dose PCT images. Specially, the PCT image sequence is firstly divided into two parts: 2D non-enhanced baseline image part which is regarded as the background information and 3D enhanced sequence part which is regarded as the enhanced information. Then these two parts are processed via DL procedures for 2D background and 3D enhanced information, respectively. Finally the restored PCT images are obtained through combining the restored baseline images with the restored enhanced information. In the following section, we describe the CDL procedure in detail.

2.2.1 DL for 2D background information

In the 2D background DL, the objective 2D non-enhanced baseline image is obtained by averaging the previous low-dose unenhanced PCT scans which is defined as Y^b. To obtain high-quality objective image, a simple 2D DL processing is performed by solving the following two minimization problems: $min_{D^{b}, α^{b}} \sum_{s} {∥ α_{s}^{b} ∥}_{0} s . t . {∥ R_{s} X^{b} - D^{b} α_{s}^{b} ∥}_{2}^{2} \leq ɛ, \forall s$ (5) $min_{X^{b}} {∥ X^{b} - Y^{b} ∥}_{2}^{2} + λ_{s} \sum_{s} {∥ R_{s} X^{b} - D^{b} α_{s}^{b} ∥}_{2}^{2}$ (6) where X^b is the restored baseline image, R_s is the 2D image patch extracting operator, D^b and α^b are the corresponding dictionary and coefficients trained from a set of baseline image patches, λ_s is the regularization parameter.

2.2.2 DL for 3D enhanced information

The 3D enhanced images are produced by subtracting averaged baseline image from enhanced PCT scans individually. Considering the serious noise in the low-dose perfusion enhanced information, we propose to train the 3D enhanced dictionary from the prior normal-dose perfusion enhanced information. Given the known normal-dose perfusion enhanced information Z^e, the 3D enhanced dictionary $D_{p}^{e}$ can be predetermined through minimizing the following problem: $min_{D_{p}^{e}, α^{p}} \sum_{v} {∥ α_{v} ∥}_{0} s . t . {∥ R_{v} Z^{e} - D_{p}^{e} α_{v}^{p} ∥}_{2}^{2} \leq ɛ, \forall v$ (7) where α^p are the coefficients with respect to the dictionary $D_{p}^{e}$ , R_v is the 3D volume patch extracting operator, v denotes the 3D volume patch index.

With a pre-calculated 3D enhanced information dictionary $D_{p}^{e}$ , the 3D DL processing for low-dose enhanced information Y^e can be written as follows: $min_{α^{e}} \sum_{v} {∥ α_{v}^{e} ∥}_{0} s . t . {∥ R_{v} X^{e} - D_{p}^{e} α_{v}^{e} ∥}_{2}^{2} \leq ɛ, \forall v$ (8) $min_{X^{e}} {∥ X^{e} - Y^{e} ∥}_{2}^{2} + λ_{v} \sum_{v} {∥ R_{v} X^{e} - D_{p}^{e} α_{v}^{e} ∥}_{2}^{2}$ (9) where X^e denotes the restored low-dose enhanced information, and α^e is the sparse representation coefficients of X^e with respect to the dictionary $D_{p}^{e}$ , and λ_v is the regularization parameter.

2.2.3 PCT images restoration via CDL scheme

Figure 1 shows the corresponding 2D background and 3D enhanced dictionaries. The resultant low-dose PCT image sequence can be finally obtained by combining the restored baseline image with the restored enhanced information. In summary, given the pre-calculated dictionaries D^b and $D_{p}^{e}$ , the CDL processing for low-dose PCT imaging can be written as follow:

$\begin{matrix} min_{X, D_{p}^{e}, D^{b}, α^{e}, α^{b}} {∥ X - Y ∥}_{2}^{2} + λ_{v} \sum_{v} ({∥ R_{v} X^{e} - D_{p}^{e} α_{v}^{e} ∥}_{2}^{2} + γ_{v} {∥ α_{v}^{e} ∥}_{0}) \\ + λ_{s} \sum_{s} ({∥ R_{s} X^{b} - D^{b} α_{s}^{b} ∥}_{2}^{2} + γ_{s} {∥ α_{s}^{b} ∥}_{0}) \\ + β \sum_{t} {∥ X_{t} - X_{t}^{e} - X^{b} ∥}_{2}^{2} \end{matrix}$ (10) where X = {X₁, X₂, …, X_T} and Y = {Y₁, Y₂, …, Y_T} denote the restored and original low-dose PCT image sequences with T frames, respectively. Notice that the dictionary $D_{p}^{e}$ and the dictionary D^b are predetermined, γ_v and β are the Lagrange multiplier and regularization parameter, respectively. Equation (10) can be solved by using the following sub-optimization formulas: $\begin{matrix} P 1 : min_{α^{e}} \sum_{v} {∥ α_{v}^{e} ∥}_{0} s . t . {∥ R_{v} X^{e} - D_{p}^{e} α_{v}^{e} ∥}_{2}^{2} \leq ɛ, \forall v \\ P 2 : min_{α^{b}} \sum_{s} {∥ α_{s}^{b} ∥}_{0} s . t . {∥ R_{s} X^{b} - D^{b} α_{s}^{b} ∥}_{2}^{2} \leq ɛ, \forall s \\ P 3 : min_{X} {∥ X - Y ∥}_{2}^{2} + λ_{v} \sum_{v} {∥ R_{v} X^{e} - D_{p}^{e} α_{v}^{e} ∥}_{2}^{2} + λ_{s} \sum_{s} {∥ R_{s} X^{b} - D^{b} α_{s}^{b} ∥}_{2}^{2} \\ + β \sum_{t} {∥ X_{t} - X_{t}^{e} - X^{b} ∥}_{2}^{2} \end{matrix}$ (11)

The sub-problems P1 and P2 are in essence DL-based problems, and can be solved with the classical K-SVD method [35, 36]. The sub-problem P3 can be solved by setting derivative of sub-problem P3 equal to zero with respect to X [32]. In summary, the overall CDL scheme for low-dose PCT images restoration is illustrated in Fig. 2.

2.3 Experimental data acquisitions

To validate and evaluate the performance of the present algorithm for PCT imaging, clinical data is analyzed in this paper. Under written informed consent, a patient with an old infarction was scanned with a Siemens 64-slice multi-detector CT scanner without table movement. First, a pre-contrast unenhanced scan of the whole brain was performed with a tube current of 240 mA, and tube voltage of 80 kV p. Then, 50 ml of Iopromide 370 (Ultravist, Schering, Germany) was injected at a rate of 5.0 ml/s. The cine (continuous) enhanced normal-dose scan was performed with the following protocol: 200 mA, 80 kV p, slice thickness of 8.0 mm, 1 s per rotation for duration of 39 s, and reconstruction kernel of H30s. The other scanning imaging parameters are the same as that described in our previous work [17].

Because repetitive scanning of the same patient at different radiation doses is unethical, in this study we simulated the low-dose cerebral perfusion enhanced PCT images from the acquired normal-dose enhanced images using the simulation method described in our previous work [17]. The CTDIvol for the simulated low-dose contrast enhanced CT data is about one-seventh of that of the normal-dose scan.

2.4 Performance evaluation

In this work, a number of image quality evaluations are conducted at different levels including qualitative visualization and quantitative metrics.

2.4.1 Qualitative visualization based evaluation

The restored images and its zoomed images of the region of interest (ROI) with different algorithms are visually compared with the normal-dose PCT images. It is known that hemodynamic functional parameters are estimated from the measurement of the temporal evolution of the concentration of contrast agent at each pixel position in the ROI, and the associated temporal evolution is usually represented by the TDC. In this work, the accuracy of the present CDL scheme was qualitatively assessed by comparison of the TDC with other existing methods.

In addition, HPM, including cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT) maps, from different algorithms were also visually compared with those from normal-dose PCT images. CBF is defined as the blood supply to the brain in a given time and is typically measured in mL/100 g/min. CBV is defined as the total volume of blood traversing a given region of brain, and measured in mL/100 g. The definition of MTT is the first moment of the probability density function of the transit times, usually measured in seconds. In particular, the HPM were calculated by using perfusion analysis software (Perfusion Mismatch Analyzer (PMA), version 3.4.0.6; Acute Stroke Imaging Standardization Group, Japan, http://asist.umin.jp/index-e.htm) [41]. A standard SVD method was selected in the PMA.

2.4.2 Quantitative metrics based evaluation

Three metrics are used to quantitatively evaluate the performance of the different methods in the estimated CBF maps: (1) global root mean square error (RMSE), which is used to characterizes the restoration accuracy; (2) global peak signal to noise ratio (PSNR), which is used to measure the denoising performance; (3) local universal quality index (UQI), which measures the similarity of two images [42]. Mathematically, the three metrics are defined as follows: $RMSE = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} {(f_{i} - {\bar{f}}_{i})}^{2}}$ (12) $PSNR = 20 {log}_{10} (\frac{{\bar{f}}_{max}}{σ})$ (13) $UQI = \frac{2 Cov (f, \bar{f})}{σ_{f}^{2} + σ_{\bar{f}}^{2}} \frac{2 μ_{f} μ_{\bar{f}}}{μ_{f}^{2} + μ_{\bar{f}}^{2}}$ (14) where f represents the estimated low-dose CBF map, and $\bar{f}$ denotes the corresponding normal-dose CBF map which is used as the reference standard. n represents the number of the voxels included. σ is the corrupting noise between the reference standard and enhanced image and ${\bar{f}}_{max}$ is the maximum intensity value in the reference image. $σ_{f}^{2}$ and $σ_{\bar{f}}^{2}$ are the variances of the aligned ROI in the estimated image and reference image, respectively. μ_f and $μ_{\bar{f}}$ are the mean values in the ROIs of the estimated map and the reference map, respectively.

2.5 Comparing methods

To validate and evaluate the performance of the present CDL scheme, we selected three similar dictionary methods, named as the single-frame DL method (DL), single-frame DL method with a normal-dose image induced prior (DL-p), and sequential temporal-frame DL method (DL-t), respectively. Specifically, the DL method deals with the single-frame image separately, and the dictionary is learned from the PCT image itself without considering normal-dose image prior or temporal-frame information. Different from the DL method, the DL-p method trains the 2D dictionaries from the normal-dose PCT images and restores the low-dose PCT images frame by frame. For the DL-t method, the temporal information within the low-dose PCT images is considered, and the low-dose PCT image sequence is treated as a whole in 3D dictionaries training and image restoration [43]. The present CDL method considers not only the normal-dose prior information but also the temporal information within the normal-dose PCT image sequence.

3 Results

3.1 Visualization-based evaluation

Figure 3 shows the 20th time-frame enhanced PCT images, including the normal-dose reference image, simulated low-dose FBP image, the low-dose images restored by the DL, DL-p, DL-t and present CDL methods, respectively. It can be seen that all the images restored by the DL-based methods outperformed the simulated low-dose FBP image in terms of noise and artifacts suppression wherein severe noise-induced artifacts appeared in the simulated low-dose FBP image (Fig. 3(b)). As for the four DL-based methods, the CDL scheme is superior to the other three methods in terms of TDC and HPM measurements, which will be discussed subsequently.

3.2 TDC measurement

Figure 4 shows the TDCs of the tissue perfusion indicated by the red squares in Fig. 3 from dynamic PCT images acquired by different methods. It can be observed that the present CDL scheme produces a closer TDC to that from the normal-dose PCT images in comparison with the other methods. For a better illustration of the performance of the present CDL scheme, Fig. 5 shows the TDCs from the 15th to 25th time-frames. As we can see, the CDL result exhibits the best match with the one from the FBP reconstructed normal-dose sequential image without unrealistic oscillation.

3.3 HPM evaluation

Figure 6 shows the HPM (i.e., CBF, CBV, and MTT) estimated from the original normal-dose images and the low-dose PCT images restored by different methods. The first row shows the HPM estimated from the normal-dose PCT images, which is used as ground-truth for comparison. The second row shows the HPM estimated from the low-dose PCT images, which is also set as the baseline for comparison purpose. The third row shows the HPM derived from the DL method. It can be seen that the noise can be slightly suppressed, but the detailed structure information is still corrupted by noise-induced artifacts, especially in the CBF map. The fourth row is the results from the DL-p method. It has almost the same performance as the DL method just with a little gain. The fifth and sixth rows show the DL-t and CDL results, respectively. It can be observed that the perfusion maps generated from the two methods are comparable and match well with the ground-truth, which indicates that the temporal-frame information is very useful for developing sound dictionary-based PCT image restoration method. It is worth to note that the presented CDL method can yield remarkable gains over the DL-t method in preserving sharper edges and higher contrast between vessels and soft tissues.

3.4 Quantitative evaluation

To evaluate the performance of different methods, three metrics, including noise reduction assessment (i.e., global RMSE and PSNR) and the reconstruction accuracy of ROIs (as indicated by white squares in Fig. 6) with detailed structures (i.e., local UQI) in CBF maps, were employed. Table 1 lists the corresponding quantitative results based on the three different metrics (i.e., global RMSE, global PSNR, and local UQI). We can again observe that the present CDL scheme can yield the lowest RMSE and the highest PSNR and UQI, indicating that the present CDL scheme can derive better HPM than other methods.

In addition, to further demonstrate the benefits of the present CDL scheme quantitatively, in this study we selected 20 specific ROIs manually in Fig. 6(a) which exclude major blood vessel branches and suspected abnormal regions. These ROIs were located at both the hemispheres in basal ganglia, gray and white matter. Figure 7 illustrates the correlation coefficients and regression equation plots of CBF values under different conditions. Since the MTT should be first analyzed because it shows the most prominent regional abnormalities and facilitates depiction of the ischemic area, we add the correlation coefficients and regression equation plots of MTT values within the old infarction region (in Fig. 8) to demonstrate that the benefit of the proposed CDL scheme to improve the diagnosis or visualization of the infarction. It can be observed that the correlation coefficient derived from the normal-dose images and the low-dose images restored by the CDL scheme is higher than those from the low-dose images restored by other methods. It can be concluded that the present CDL scheme can achieve noticeable performance in low-dose PCT HPM estimation with the accuracy of diagnostic physiological parameters. In other words, the present CDL scheme outperforms the other methods not only in terms of PCT image quality, but also with regard to the HPM estimation

4 Discussion and conclusion

In this paper, we developed an image restoration model via a new CDL scheme. With this scheme, a pair of dictionaries is learned from unenhanced/enhanced image information patches. One is able to describe unenhanced/background information patches, and the other can represent enhanced information ones. For the PCT image sequence, it can be divided into two parts: two-dimension (2D) background part and three-dimension (3D) enhanced part and then the 2D background part and 3D enhanced part are used to build the background dictionary and enhanced dictionary, respectively. In this study, the patch size of 2D background dictionary is set as 8 × 8, the patch size of 3D enhanced dictionary is set as 8 × 8 ×8, and the number of atoms is 256 for both dictionaries. One motivation is that the proposed CDL scheme exploits both the rich redundancy with the background information and the spatio-temporal information with the enhanced information of cerebral PCT images to train the pair of dictionaries. Considering the high noise level of low-dose PCT image sequence, we trained the enhanced information dictionary from the previous normal-dose PCT dataset while the background dictionary was trained from the baseline image by averaging the image frames before enhancement. The present CDL scheme was evaluated using one set of clinical dataset. The experimental results have demonstrated the present CDL scheme outperformed the other state-of-the-art methods in not only noise-induced artifacts suppression, but also HPM estimation.

It is worth to note that there are several limitations for the present CDL scheme. The first is the parameter tuning. It is known that optimizing all the parameters is a difficult but interesting task for almost all the regularized reconstruction/restoration problems. In our study, three parameters, i.e., λ_v, λ_s and β, control the tradeoff between the data fidelity and the penalty term. In order to choose the best values, we applied a range of set of parameters and selected the set of parameters based on heuristic guidelines, such as yielding the best eye-appealing results. Further investigation on parameter selection is need for realistic applications, which is a topic in our further research plan. Secondly, we acknowledge the limited number of patient cases for evaluating the present CDL scheme in this work. To further validate the present CDL scheme, we should involve larger samples including different cerebrovascular diseases and patient variety for widespread clinical application in our future research. Last but not least, the HPM were calculated by the SVD-based deconvolution algorithm. It is well known that the SVD-based deconvolution algorithms treat all the tissue voxel independently. In fact, the physiological changes to perfusion are regional effects and temporal information should be taken into consideration. At the same time, the SVD- based deconvolution algorithms are sensitive to noise, resulting in introducing unwanted oscillation easily [44, 45]. However, there are some advanced image-based deconvolution algorithms, which have been shown to significantly improve its performance, such as Bayesian probabilistic deconvolution framework [21], DL-based deconvolution framework [22] and total variation regularization deconvolution methods [23]. Further researches are needed to validate the effectiveness of combining the CDL scheme with other advanced deconvolutionmethods.

In this work, we presented an image restoration method by utilizing CDL scheme to yield a clinically acceptable cerebral PCT images with low-mAs data acquisition. The experimental result with one set of clinical cerebral PCT data has shown its effectiveness and potential in clinical practice. Given that a large number of existing normal-dose clinical cerebral PCT data has been collected for training the dictionaries in the present CDL scheme, the new patient just needs to go through the low-dose scanning for the cerebral perfusion examination with guaranteed diagnostic quality. And it will be the start of a constructive and meaningful work in clinic. While our work has been presented in the context of cerebral PCT, the present CDL scheme could be potentially extended to other clinical applications, such as dynamic myocardial perfusion CT [46], 4D CT imaging [47], PET imaging [37], and MR imaging [48].

Footnotes

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 81371544, 61571214, 81501466, and 81501541, the National Science and Technology Major Project of the Ministry of Science and Technology of China under Grant No. 2014BAI17B02, the Guangdong Natural Science Foundation under Grant Nos. 2015A030313271, 2014A030310243, and 2015A030310018, the Science and Technology Program of Guangdong, China under Grant Nos. 2015B020233008 and 2015A030401039, the Science and Technology Program of Guangzhou, China under Grant No. 201510010039, and the Scientific Research Foundation of Southern Medical University, Guangzhou, China under Grant No. CX2015N002.

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