DuDoSS: Deep-Learning-Based Dual-Domain Sinogram Synthesis from Sparsely-Sampled Projections of Cardiac SPECT

Abstract

Purpose:

Myocardial perfusion imaging (MPI) using single-photon emission computed tomography (SPECT) is widely applied for the diagnosis of cardiovascular diseases. In clinical practice, the long scanning procedures and acquisition time might induce patient anxiety and discomfort, motion artifacts, and misalignments between SPECT and computed tomography (CT). Reducing the number of projection angles provides a solution that results in a shorter scanning time. However, fewer projection angles might cause lower reconstruction accuracy, higher noise level, and reconstruction artifacts due to reduced angular sampling. We developed a deep-learning-based approach for high-quality SPECT image reconstruction using sparsely-sampled projections.

Methods:

We proposed a novel deep-learning-based dual-domain sinogram synthesis (DuDoSS) method to recover full-view projections from sparsely-sampled projections of cardiac SPECT. DuDoSS utilized the SPECT images predicted in the image domain as guidance to generate synthetic full-view projections in the sinogram domain. The synthetic projections were then reconstructed into non-attenuation-corrected (NAC) and attenuation-corrected (AC) SPECT images for voxel-wise and segment-wise quantitative evaluations in terms of normalized mean square error (NMSE) and absolute percent error (APE). Previous deep-learning-based approaches including direct sinogram generation (Direct Sino2Sino) and direct image prediction (Direct Img2Img) were tested in this study for comparison. The dataset used in this study included a total of 500 anonymized clinical stress-state MPI studies acquired on a GE NM/CT 850 scanner with 60 projection angles following the injection of ^99mTc-tetrofosmin.

Results:

Our proposed DuDoSS generated more consistent synthetic projections and SPECT images with the ground truth than other approaches. The average voxel-wise NMSE between the synthetic projections by DuDoSS and the ground-truth full-view projections was 2.08 ± 0.81%, as compared to 2.21 ± 0.86% (p < 0.001) by Direct Sino2Sino. The averaged voxel-wise NMSE between the AC SPECT images by DuDoSS and the ground-truth AC SPECT images was 1.63 ± 0.72%, as compared to 1.84 ± 0.79% (p < 0.001) by Direct Sino2Sino and 1.90 ± 0.66% (p < 0.001) by Direct Img2Img. The averaged segment-wise APE between the AC SPECT images by DuDoSS and the ground-truth AC SPECT images was 3.87 ± 3.23%, as compared to 3.95 ± 3.21% (p = 0.023) by Direct Img2Img and 4.46 ± 3.58% (p < 0.001) by Direct Sino2Sino.

Conclusions:

Our proposed DuDoSS is feasible to generate accurate synthetic full-view projections from sparsely-sampled projections for cardiac SPECT. The synthetic projections and reconstructed SPECT images generated from DuDoSS are more consistent with the ground-truth full-view projections and SPECT images than other approaches. DuDoSS can potentially enable fast data acquisition of cardiac SPECT.

1. INTRODUCTION

Myocardial perfusion imaging (MPI) using single-photon emission computed tomography (SPECT) is the most widely performed nuclear cardiology exam that allows sensitive detection, localization, and risk stratification of ischemic heart disease.^1–3 In clinical practice, cardiac SPECT imaging using rotational scanners generally involves detectors rotating around the chest in a step-and-shoot protocol to acquire the projection data. The long scanning procedures and acquisition time present challenges that hinder efficient and accurate clinical exams. First, patients undergoing complex imaging examinations such as hybrid SPECT-CT might experience anxiety and discomfort due to the long scanning time.⁴ This will increase the likelihood of noncompliance during the imaging procedures, leading to suboptimal scans and inaccurate reports.^{5, 6} Second, body motion during a long scanning time might cause motion artifacts and further affect the diagnostic accuracy.^7–9 Voluntary or involuntary body motions during the data acquisition procedure might cause significant displacements of hearts or other organs, which will cause misregistration of projection data. Excessive movements may require repeated scans with additional radiation exposure to patients. Third, SPECT and CT images are acquired sequentially and the displacements of the patient body during the long acquisition time might lead to misalignment of SPECT and CT scans, thus creating attenuation correction artifacts.^10–12 Last, SPECT imaging in a large volume clinical lab requires efficiency of imaging.^{13, 14} Therefore, shorter imaging times could increase the patient throughput in a busy lab.

Reducing the number of projection angles provides a solution that results in a shorter scanning time. However, fewer projection angles can lead to lower reconstruction accuracy, higher noise level, and severe artifacts due to the reduced angular sampling.^15–17 Thus, compensating the image quality degradation under the premise of sparsely-sampled projections is an important topic to investigate. Sparse-view image reconstruction is a widely explored application in CT.^{18, 19} The evolving deep learning techniques has provided solutions to this important topic in CT.^20–24 However, the sparse-view sinogram recovery or sinogram inpainting in PET and SPECT is still under explored. Prior conventional works in sinogram inpainting and synthesis of PET and SPECT included sparse presentation-based methods that applied dictionary learning for sparse representation and data recovery of PET sinogram,^25–27 compressive sensing-based methods based on wavelet-domain total variation minimization to recover missing data in PET acquisition,²⁸ and model-based reconstruction methods that combined the estimation maximization algorithm with mixed region and voxel image representation,²⁹ etc. For deep-learning-based methods, U-Net³⁰ was applied to inpaint the missing data in the sinogram of whole-body PET in a previous study.³¹ The experiment was implemented in the sinogram domain, in which the defective sinogram was input to U-Net to predict the intact sinogram. In another study, ResNet³² was applied to generate synthesis projections from half-time or sparse-view sampled projections of cardiac SPECT, which was implemented in sinogram domain.³³ Another study implemented the PET sinogram recovery in either sinogram domain or image domain, in which the defective sinogram or the PET image was input to U-Net to predict the complete sinogram or image.³⁴ A novel deep learning framework LU-Net combining Long Short-Term Memory network (LSTM)³⁵ and U-Net was proposed for the sparse-view SPECT sinogram synthesis.³⁶ Due to the embedded LSTM modules, the LU-Net has a larger receptive field since it can exploit the projection data in both neighboring and distant view angles.

A recent method named convolutional U-Net-shaped synthetic intermediate projections (CUSIP) generated synthetic projections (120 angles) from sparsely-sampled projections (30 angles) for ¹⁷⁷Lu SPECT images.³⁷ In CUSIP, three separate neural networks were independently trained to predict three sets of 30 intermediate projections, which were then combined with the input sparsely-sampled projections to generate the predicted full-view projections (120 angles). However, this method predicted each set of projections separately, which did not incorporate the 3D spatial information of image volumes into neural networks.

The aforementioned deep learning methods were implemented in either image or sinogram domain, and none of them has combined the information of both image and sinogram domains for the sparse-view sinogram recovery of PET or SPECT. The dual-domain strategy has widely used in many fields of medical imaging including reconstruction,^{38, 39} CT metal artifact reduction,^{40, 41} segmentation,^{42, 43} image synthesis,^{44, 45} etc., but it has not been investigated in the sparse-view sinogram recovery of PET or SPECT yet. In this study, we proposed a deep-learning-based Dual-Domain Sinogram Synthesis (DuDoSS) method to predict the synthetic full-view projections from sparsely-sampled projections of cardiac SPECT.

2. MATERIALS AND METHODS

2.1. Study datasets

The dataset used in this study included a total of 500 anonymized clinical stress SPECT MPI studies acquired on a GE NM/CT 850 scanner with 60 projection angles. The projection data were acquired using a step-and-shoot protocol over 360 degrees with a parallel head (H-mode) configuration. The patient studies were anonymized and exported from the clinical PACS using the AI Accelerator (Visage Imaging, Inc., San Diego, CA). One-day stress-only low-dose protocol was used with the mean administered dose of 15 mCi ^99mTc-tetrofosmin. Among the 500 patient studies, 250, 100, 150 were used for training, validation, and testing, respectively. The patient information including gender, age, height, weight, and BMI distribution are listed in Table 1.

TABLE 1.

The gender, age, height, weight, and BMI distribution of the enrolled patients.

Patient Information		Age (year)	Height (m)	Weight (kg)	BMI
Training Data (132 M, 118 F)a	Range	34 – 94	1.42 – 1.90	44.50 – 150.1	16.35 – 49.98
	Mean ± Std.	64.79 ± 11.35	1.69 ± 0.11	87.09 ± 19.08	30.66 ± 6.16
Validation Data (50 M, 50 F)	Range	39 – 96	1.45 – 1.93	42.20 – 159.2	17.69 – 49.14
	Mean ± Std.	63.37 ± 11.91	1.67 ± 0.12	88.89 ± 21.00	31.67 ± 6.21
Testing Data (86 M, 64 F)	Range	37 – 94	1.42 – 1.93	19.10 – 160.7	17.66 – 46.63
	Mean ± Std.	67.90 ± 12.31	1.69 ± 0.11	84.34 ± 21.23	29.49 ± 5.71

^aM stands for male and F stands for female.

Clinical imaging with the GE NM/CT 850 involves full-view projections with a dimension of 64×64×60 and a voxel size of 6.8×6.8×6.8 mm³ acquired in a photopeak window (126.5 – 154.5 keV). The CT-derived attenuation maps were all manually checked and registered with SPECT images by technologists at Yale Nuclear Cardiology Clinic using GE’s ACQC package.

2.2. Image preprocessing and reconstructions

To reduce the number of projection angles, the 60 angles were evenly divided into four sparsely-sampled sub-datasets. Each sub-dataset with a dimension of 64×64×15 consisted of 15 projections. The four sub-datasets were formed by selecting every first, second, third, and fourth projections of the full-view 60 projections, which were labeled as Angles 1, 2, 3, and 4. In the CUSIP approach,³⁷ Angle 1 was used as the input to three individual U-Nets with different trainable parameters to predict Angles 2, 3, and 4 independently. In our DuDoSS approach, the input Angle 1 was zero-padded into the dimension of 64×64×60 and then used as the input to the networks.

The sparsely-sampled (64×64×15) or full-view (64×64×60) projections were reconstructed into SPECT images (64×64×64) using Maximum-Likelihood Expectation-Maximization (MLEM, 120 iterations, no scatter correction) and Butterworth filter (cutoff frequency = 0.37 cm⁻¹, order = 7). Non-attenuation-corrected (NAC) and AC SPECT images were reconstructed without or with the incorporation of the CT-derived attenuation maps, respectively.

Analyzing the specific regions of interest (ROI) is quite important for medical imaging. However, in cardiac SPECT, the tracer distributions outside the cardiac regions, especially at the abdomen, are sometimes extremely high, which might affect the quantitative evaluations of hearts. Thus, we cropped 32 slices out of the original 64 slices along the z axis of the full-view projections, to include the cardiac regions and exclude the background signals. The size of the full-view projections was cropped from 64×64×60 into 64×32×60. Similarly, the size of the SPECT images was cropped from 64×64×64 into 64×64×32. In our experiment, we utilized the cropped projections and images for the network training, testing, and quantitative evaluations, to reduce the effect of the background signals.

2.3. Overview of DuDoSS

Figure 1 shows the diagram of our proposed DuDoSS approach. The general principle was utilizing the predicted full-view images as guidance to generate the synthetic full-view projections. The overall workflow included image-domain prediction using an image-domain networks ImgNet, domain transitions using a forward-projection operator, and sinogram-domain generation using a sinogram-domain networks SinoNet.

FIGURE 1.

Diagram of DuDoSS. X_sparse reconstructed using sparsely-sampled projections S_sparse was input to the ImgNet to predict the full-view SPECT image X_full−pred. Then, X_full−pred was forward-projected to generate a prior full-view projections S_prior, which were then combined with the ground-truth acquired Angle 1 to obtain S_{prior−combine}. Next, S_{prior−combine} was input to the SinoNet to generate the predicted sinogram S_pred. Finally, S_pred was combined with the ground-truth acquired Angle 1 to output the combined projections S_{pred−combine}.

First, the zero-padded sparsely-sampled projections S_sparse were reconstructed into a sparsely-reconstructed image X_sparse using MLEM. In the image domain, X_sparse was input to ImgNet to generate the predicted full-view image X_full−pred, formulated as:

$$X_{\mathit{\text{full}}-\mathit{\text{pred}}}=f_{\mathit{\text{Img}}}(X_{\mathit{\text{sparse}}}),$$ (1)

where f_Img denoted the image prediction using ImgNet. L1 loss is a robust mean-based measurement that does not over-penalize significant errors nor tolerate subtle errors. Thus, to optimize ImgNet, we employed L1 loss to minimize the difference between X_full−pred and X_full which was reconstructed using the ground-truth full-view projections, formulated as:

$${ℒ}_{\mathit{\text{Img}}}={\Vert X_{\mathit{\text{full}}-\mathit{\text{pred}}}-X_{\mathit{\text{full}}}\Vert }_1,$$ (2)

where ℒ_Img denoted the image-domain loss. Then, the predicted X_full−pred was forward-projected to generate the prior full-view projections S_prior, formulated as:

$$S_{\mathit{\text{prior}}}=𝒫\left(X_{\mathit{\text{full}}-\mathit{\text{pred}}}\right),$$ (3)

where 𝒫 referred to the forward-projection operator. S_prior was utilized as a prior estimate of the ground-truth full-view projections S_full. Then, Angle 1 of S_prior was replaced by the ground-truth acquired Angle 1 in a combination module to further improve the accuracy of the projections, formulated as:

$$S_{\mathit{\text{prior}}-\mathit{\text{combine}}}=S_{\mathit{\text{sparse}}}+S_{\mathit{\text{mask}}}\ast S_{\mathit{\text{prior}}},$$ (4)

where * denoted the element-wise multiplications. S_{prior−combine} referred to the combined projections. S_mask was a binary mask with value 0 in Angle 1 and value 1 at Angles 2, 3, and 4.

Next, in the sinogram domain, S_{prior−combine} was input to SinoNet to generate the synthetic full-view projections S_pred, formulated as:

$$S_{\mathit{\text{pred}}}=f_{\mathit{\text{Sino}}}\left(S_{\mathit{\text{prior}}-\mathit{\text{combine}}}\right),$$ (5)

where f_Sino referred to the sinogram generation using SinoNet. Finally, Angle 1 of S_pred was replaced by the ground-truth acquired Angle 1 in a combination module to further improve the accuracy of the synthetic projections, formulated as:

$$S_{\mathit{\text{pred}}-\mathit{\text{combine}}}=S_{\mathit{\text{sparse}}}+S_{\mathit{\text{mask}}}\ast S_{\mathit{\text{pred}}}.$$ (6)

To optimize SinoNet, we employed L1 loss to minimize the difference between S_{pred−combine} and the ground-truth full-few projections S_full, formulated as

$${ℒ}_{\mathit{\text{Sino}}}={\Vert S_{\mathit{\text{pred}}-\mathit{\text{combine}}}-S_{\mathit{\text{full}}}\Vert }_1,$$ (7)

where ℒ_Sino denoted the sinogram-domain loss.

In our study, we jointly trained the ImgNet and SinoNet in an end-to-end manner and the total objective loss function is formulated as

$${ℒ}_{\mathit{\text{Total}}}={ℒ}_{\mathit{\text{Img}}}+{ℒ}_{\mathit{\text{Sino}}}.$$ (8)

In this workflow, both ImgNet and SinoNet were Dual-Squeeze-and-Excitation Residual Dense Network (DuRDN) which was proposed in one of our previous works and showed superior performance than U-Net in some image transformation tasks.⁴⁶ DuRDN was built using Residual Dense Blocks (RDB) and Dual Squeeze-and-Excitation (DuSE) self-attention modules. RDB effectively extract the image information using densely-connected structures and global residual connections. DuSE encouraged the networks to recalibrate both channel-wise and spatial features such that more accurate and relevant feature maps can be learned.

2.4. Experiments

In our experiment, the original full-view projections and the SPECT images reconstructed using the original full-view projections were considered as the ground truth. The CUSIP approach was tested as the benchmark in this study, labeled as CUSIP. Alternatively, we implemented another CUSIP by replacing the U-Net by DuRDN, which was labeled as CUSIP-DuRDN.

We tested two additional ablation study groups, labeled as Direct Sino2Sino and Direct Img2Img. The detailed schematics of Direct Sino2Sino and Direct Img2Img are presented in Section 1 of Supplementary Materials. The Direct Sino2Sino was implemented only in the sinogram domain. The zero-padded sparse-view projections S_sparse were input to the SinoNet to predict the synthetic full-view projections S_pred, with the ground-truth full-view projections S_full as targets. Then, Angle 1 of S_pred was replaced by ground-truth Angle 1 to produce S_{pred−combine} for the reconstruction of the predicted full-view SPECT image. Direct Img2Img was implemented only in the image domain, without any intermediate step of synthetic projections. The SPECT image X_sparse reconstructed using S_sparse was input to the ImgNet to directly generate the predicted full-view image X_full−pred, with the ground-truth full-view image X_full as targets.

2.5. Network training

All the hyperparameters including learning rates, learning rate decay rates, batch sizes, have been optimized to maximize the performance for each testing group after repeated experiments. To maintain the spatial integrity of the sinogram, we did not implement patch-based strategies and the entire image volumes were used as input and output in this study.

In the CUSIP, CUSIP-DuRDN, and Direct Sino2Sino group, U-Net or DuRDN were trained for 600 epochs with a learning rate of 5×10⁻⁴, a batch size of 4, and an Adam optimizer (exponential decay rates β₁ = 0.5, β₂ = 0.999). A learning rate decay policy with a step size of 1 and a decay rate of 0.99 was employed to avoid overfitting.⁴⁷ In the Direct Img2Img group, the learning rate was 5×10⁻⁴, and other hyperparameters were the same as above. In our proposed DuDoSS, the learning rates of ImgNet and SinoNet were 1×10⁻⁵ and 1×10⁻⁴ respectively. The other parameters were the same as above.

The numbers of trainable parameters in CUSIP, CUSIP-DuRDN, Direct Sino2Sino, Direct Img2Img, and DuDoSS were respectively about 2 m, 2.5 m, 2.5 m, 2.5 m, and 5 m (m: million). DuDoSS contained the most trainable parameters because it had two end-to-end connected networks. The consumed memories during the training process of CUSIP, CUSIP-DuRDN, Direct Sino2Sino, Direct Img2Img, and DuDoSS were about 3 GB, 4 GB, 7 GB, 7.5 GB, and 12 GB (GB: gigabytes). Under the same hardware support of the NVIDIA Quadro RTX 8000 graphic card, the training time of CUSIP was about 4 hours for each angle and 12 hours in total, and the training time of CUSIP-DuRDN was about 7 hours for each angle and 21 hours in total. The total training time of Direct Sino2Sino, Direct Img2Img, and DuDoSS were 9 hours, 10 hours, and 16 hours, respectively. CUSIP-DuRDN group consumed the longest training time to converge. For every testing group, the testing time of each case was shorter than 0.1 second, which was a reasonable inference time for clinical practice.

2.6. Voxel-wise quantitative evaluations

The voxel-wise quantitative evaluation metrics used in this study included normalized mean square error (NMSE), normalized mean absolute error (NMAE), structural similarity (SSIM),⁴⁸ and peak signal-to-noise ratio (PSNR). NMSE, NMAE, PSNR are defined as:

$$\mathit{\text{NMSE}}=\frac{{\sum }_{i=1}^N{\left(X_i-Y_i\right)}^2}{{\sum }_{i=1}^N{Y}_i^2},$$ (9)

$$\mathit{\text{NMAE}}=\frac{{\sum }_{i=1}^N\left|X_i-Y_i\right|}{{\sum }_{i=1}^N\left|Y_i\right|},$$ (10)

$$\mathit{\text{PSNR}}=10\times {\mathit{\text{log}}}_{10}\left(\frac{\mathit{\text{Max}}{\left(Y\right)}^2}{{\sum }_{i=1}^N{\left(X_i-Y_i\right)}^2}\right),$$ (11)

where X_i and Y_i are the i^th voxels of the predicted image and ground-truth image. N is the total number of voxels of the image volume. Max(Y) is the maximum voxel value of the ground-truth image. SSIM is defined as:

$$\mathit{\text{SSIM}}\left(X,Y\right)=\frac{\left(2{\mu }_Y{\mu }_X+C_1\right)\left(2{\sigma }_{YX}+C_2\right)}{\left({\mu }_Y^2+{\mu }_X^2+C_1\right)\left({\sigma }_Y^2+{\sigma }_X^2+C_2\right)},$$ (12)

where C₁ = (K₁ × R)² and C₂ = (K₂ × R)² are constants to stabilize the ratios. R stands for dynamic range of pixel values. Usually, we set K₁ = 0.01 and K₂ = 0.03. μ_X and μ_Y are the means of Y and X. ${\sigma }_Y^2$ and ${\sigma }_X^2$ are the variances of Y and X. σ_YX is the covariance of Y and X.

The calculation of NMSE/NMAE/PSNR/SSIM should be restricted within the region containing the patient heart to eliminate the influence of background signals or artifacts. Thus, we generated binary image masks by thresholding to restrict quantitative evaluations within the voxels of the patient heart. Then, we applied forward projection of the binary image masks to generate the binary sinogram masks that restrict the quantitative evaluations within the cardiac sinogram regions. The images or sinograms were element-wise multiplied with the binary image or sinogram masks before the quantitative evaluations using NMSE/NMAE/PSNR/SSIM. The sample binary masks for quantitative evaluations of images and sinograms are provided in Section 2 of Supplementary Materials.

The synthetic projections were compared with the ground-truth full-view projections. The SPECT images reconstructed with the synthetic projections are compared with the images reconstructed with the ground-truth full-view projections. Both AC and NAC SPECT images were involved in the voxel-wise quantitative evaluations.

2.7. Segment-wise quantitative evaluations

To specifically quantify the myocardial perfusion intensities, standard 17-segment polar maps were generated for qualitative and quantitative evaluations of the NAC and AC SPECT images.⁴⁹ The mean values of segments were measured using the Carimas Software⁵⁰ for computing the segment-wise absolute percent error (APE) and percent error (PE) defined as:

$$\mathit{\text{APE}}=100\%\times {\sum }_{i=1}^{17}\left|\mathit{\text{Pre}}{d}_i-A{C}_i\right|/\left(17\times A{C}_i\right),$$ (13)

$$PE=100\%\times {\sum }_{i=1}^{17}\left(\mathit{\text{Pre}}{d}_i-A{C}_i\right)/\left(17\times A{C}_i\right),$$ (14)

where Pred_i and AC_i represent the mean values of the i^th segment in the polar maps of the predicted and ground-truth SPECT images.

2.8. Statistical analysis

For statistical analysis, two-tailed paired t-tests with a significance level of 0.05 was performed based on the above quantification metrics between two testing groups. P-values lower than 0.05 represented a significant difference of the quantification metrics between the two testing groups.

3. RESULTS

3.1. Synthetic projections

Figure 2 shows representative synthetic full-view projections. It can be observed that CUSIP and CUSIP-DuRDN under-estimated the intensities of the synthetic projections. Based on error maps of the synthetic projections, Direct Sino2Sino generated more consistent synthetic projections than the above two groups. DuDoSS provided the most consistent projections compared with the ground-truth full-view projections. Table 2 lists the voxel-wise quantitative evaluations of the synthetic projections in terms of NMSE, NMAE, SSIM, and PSNR for the 150 testing patient studies. CUSIP-DuRDN showed more accurate prediction results than CUSIP, demonstrating the superiority of DuRDN to U-Net. Direct Sino2Sino was more accurate than the above two groups. DuDoSS showed the lowest errors among all the testing groups. The significant p-values further validated that DuDoSS produced more accurate synthetic projections relative to the other groups. In addition, to test the influence of loss functions on the accuracy of the synthetic sinograms by DuDoSS, we implemented several ablation DuDoSS groups supervised by different loss functions. The results demonstrated that L1 loss was currently the most simple but effective loss function in this study, which are presented in Section 3 of the Supplementary Materials.

FIGURE 2.

Sample synthetic projections of the slice crossing the center of the patient heart. The error maps between the synthetic and ground-truth full-view projections are shown in the second row. CUSIP and CUSIP-DuRDN show obvious under-estimations of the synthetic projections. DuDoSS outputs the most consistent projections with the ground truth full-view projections compared with other testing groups. Errors between the predicted and ground-truth projections are denoted with white arrows.

TABLE 2.

Voxel-wise quantitative evaluations of the synthetic projections of the 150 testing patient studies.

Testing Groups	NMSE (×10−2)	NMAE (×10−2)	SSIM	PSNR	P-valuea
CUSIP	2.53 ± 1.04	10.91 ± 1.26	0.979 ± 0.072	35.11 ± 4.08	–
CUSIP-DuRDN	2.17 ± 0.84	10.23 ± 1.59	0.980 ± 0.075	35.82 ± 4.44	< 0.001*
Direct Sino2Sino	1.80 ± 0.82	9.22 ± 1.58	0.983 ± 0.068	36.71 ± 4.35	< 0.001*
DuDoSS (proposed)	1.65 ± 0.72	8.95 ± 1.56	0.984 ± 0.067	37.09 ± 4.51	< 0.001*

^aTwo-tailed paired t-test of NMSE between the current and previous group in the table.

^*Refers to significant difference with a significance level of 0.05.

Figure 3 provides an example of synthetic projections at three consecutive Angles 2, 3, 4. In Angles 2, 3, and 4, CUSIP and CUSIP-DuRDN both showed obvious under-estimations of the projection intensity, especially at the cardiac regions. In contrast, Direct Sino2Sino yielded more consistent projections than the above two groups. DuDoSS yielded the most consistent projections with ground truth in all 3 projection angles. In addition, Table 3 lists the quantitative evaluations of the synthetic projections at Angles 2, 3, and 4 for the 150 testing patient studies. At each projection angle, it can be observed that Direct Sino2Sino yielded more accurate projections than CUSIP and CUSIP-DuRDN. DuDoSS provided the most accurate predictions at each angle. DuDoSS predicted significantly more accurate projections than other groups in Angles 2, 3, and 4 based on the significant p-values.

FIGURE 3.

Sample synthetic projections at three consecutive Angles 2, 3, 4. The error maps between the synthetic and ground-truth corresponding projections are shown below each image. CUSIP and CUSP-DuRDN show obvious under-estimations in all angles, especially at the central cardiac regions. DuDoSS predicts the most consistent projections in all Angles 2, 3, and 4 compared with the ground-truth projections. Errors between the predicted and ground-truth projections are denoted with white arrows.

TABLE 3.

Quantitative evaluations of synthetic projections at Angle 2, 3, and 4 respectively of the 150 testing patient studies.

Testing Groups	Projection Angle 2		Projection Angle 3		Projection Angle 4
	NMSE (×10−2)	P-valuea	NMSE (×10−2)	P-valuea	NMSE (×10−2)	P-valuea
CUSIP	3.57 ± 1.26	–	3.29 ± 1.63	–	3.23 ± 1.38	–
CUSIP-DuRDN	2.89 ± 1.08	< 0.001*	2.93 ± 1.36	< 0.001*	2.86 ± 1.06	< 0.001*
Direct Sino2Sino	2.25 ± 1.02	< 0.001*	2.47 ± 1.32	< 0.001*	2.46 ± 1.13	< 0.001*
DuDoSS (proposed)	2.18 ± 0.96	0.004*	2.22 ± 1.05	< 0.001*	2.20 ± 1.03	< 0.001*

^aTwo-tailed paired t-test of NMSE between the current and previous group in the table.

^*Refers to significant difference with a significance level of 0.05.

3.2. Reconstructed SPECT images

The synthetic projections from CUSIP, CUSIP-DuRDN, Direct Sino2Sino, and DuDoSS were reconstructed into NAC and AC SPECT images using MLEM. Direct Img2Img predicted full-view SPECT images from sparsely-sampled SPECT images directly. Sample NAC and AC SPECT images are shown in Figure 4. The reconstructed NAC or AC images by CUSIP and CUSIP-DuRDN showed obvious under-estimations of the myocardial perfusion intensities due to the under-estimations of synthetic projections as presented in Figure 3. Direct Img2Img showed slightly more visually consistent NAC and AC images with ground truth than Direct Sino2Sino. In contrast, DuDoSS showed the most consistent NAC and AC SPECT images with the ground-truth full-view SPECT images.

FIGURE 4.

Sample NAC and AC SPECT images and corresponding error maps shown in the horizontal long axis (HLA) and the short axis (SA) views. The NAC SPECT images are shown in the top red dash box, and the AC SPECT images are shown in the bottom blue dash box. DuDoSS outputs the most consistent NAC and AC SPECT images with the ground-truth full-view SPECT images. Errors between the predicted and ground-truth SPECT images are denoted with white arrows.

To better quantify the myocardial perfusion intensities of the NAC and AC SPECT images, we plotted the circumferential count profiles of myocardial perfusion intensities for representative NAC and AC SPECT images as shown in Figure 5. The detailed implementation of the circumferential profiles is presented in Section 4 of Supplementary Materials. It can be observed that the profiles from DuDoSS were the most consistent with those of the ground truth for both the NAC and AC SPECT images. In contrast, the profiles of CUSIP were even worse than those from Sparse-View baseline due to the significant under-estimations of myocardial perfusion intensities in the cardiac regions.

FIGURE 5.

Circumferential count profiles of myocardial perfusion intensities of sample NAC and AC SPECT images in the SA view. The profiles of NAC and AC images are shown in the top red dash box and the bottom blue dash box. DuDoSS outputs the most consistent profiles with those of the ground-truth Full-View Recon, while CUSIP shows the highest prediction errors.

The voxel-wise quantitative evaluations of the reconstructed NAC and AC SPECT images of the 150 patient studies are provided in Tables 4 and 5. In both NAC and AC images, CUSIP produced the highest voxel-wise errors, followed by CUSIP-DuRDN. Direct Sino2Sino showed better results than Direct Img2Img, and our DuDoSS showed more consistent results than other testing groups. DuDoSS showed statistically more accurate results relative to the other testing groups based on the significant p-values.

TABLE 4.

Quantitative evaluations of the reconstructed NAC SPECT images of the 150 testing patient studies.

Testing Groups	NMSE (×10−2)	NMAE (×10−2)	SSIM	PSNR	p-valuea
Sparse-View Baseline	2.51 ± 1.58	12.73 ± 2.77	0.9948 ± 0.0020	38.81 ± 2.86	–
CUSIP	2.54 ± 1.13	13.31 ± 2.19	0.9938 ± 0.0015	38.51 ± 2.02	–
CUSIP-DuRDN	1.64 ± 0.77	10.41 ± 2.10	0.9958 ± 0.0014	40.49 ± 2.28	< 0.001*
Direct Img2Img	1.53 ± 1.05	9.77 ± 2.69	0.9965 ± 0.0014	41.00 ± 1.82	0.154
Direct Sino2Sino	1.33 ± 0.81	9.17 ± 2.25	0.9967 ± 0.0013	41.54 ± 2.23	0.003*
DuDoSS (proposed)	1.07 ± 0.67	8.29 ± 1.84	0.9974 ± 0.0010	42.45 ± 2.55	< 0.001*

^aTwo-tailed paired t-test of NMSE between the current and previous group in the table.

^*Refers to significant difference with a significance level of 0.05.

TABLE 5.

Quantitative evaluations of the reconstructed AC SPECT images of the 150 testing patient studies.

Testing Groups	NMSE (×10−2)	NMAE (×10−2)	SSIM	PSNR	P-valuea
Sparse-View Baseline	1.53 ± 0.72	9.84 ± 1.98	0.9966 ± 0.0011	41.16 ± 2.91	–
CUSIP	2.50 ± 1.03	12.99 ± 1.92	0.9938 ± 0.0013	38.89 ± 2.01	–
CUSIP-DuRDN	1.68 ± 0.86	10.20 ± 1.98	0.9958 ± 0.0014	40.72 ± 2.24	< 0.001*
Direct Img2Img	1.37 ± 0.80	9.02 ± 2.03	0.9967 ± 0.0012	41.71 ± 2.20	0.090
Direct Sino2Sino	1.28 ± 0.48	8.99 ± 1.61	0.9969 ± 0.0011	41.81 ± 2.41	< 0.001*
DuDoSS (proposed)	1.16 ± 0.71	8.30 ± 1.79	0.9973 ± 0.0011	42.43 ± 2.50	< 0.001*

^aTwo-tailed paired t-test of NMSE between the current and previous group in the table.

^*Refers to significant difference with a significance level of 0.05.

3.3. Polar maps of SPECT images

Figure 6 shows the 17-segment polar maps from representative NAC and AC SPECT images. The segment intensities of polar maps by CUSIP and CUSIP-DuRDN were under-estimated compared with the ground-truth polar maps of the full-view SPECT images. Direct Sino2Sino and Direct Img2Img produced more consistent polar maps with ground truth than the above two groups, in which the Direct Img2Img appeared slightly better. In contrast, the polar maps of DuDoSS showed polar maps that were more consistent with the ground truth than other testing groups.

FIGURE 6.

Standard 17-segment polar maps of sample NAC and AC SPECT images. The polar maps of the NAC SPECT images are shown in the top red dash box, and the polar maps of the AC SPECT images are shown in the bottom blue dash box. DuDoSS outputs the most consistent polar maps with the ground-truth polar maps of both NAC and AC SPECT images. Errors between the predicted and ground-truth polar maps are denoted with white arrows.

Figure 7 shows the correlation maps of the polar map segments between the predicted and the ground-truth full-view SPECT images of the 150 testing patient studies. For the segments of both NAC and AC images, the distributions of the correlation points using CUSIP deviated from the identity line, which produced the highest segment-wise errors. Direct Sino2Sino also showed slight deviations from the line of identity. The point distributions from Sparse-View Baseline were more dispersed than other groups. In contrast, point distributions of DuDoSS were the most concentrated along the identity line, which suggested that DuDoSS outputs the most consistent polar maps with the ground truth.

FIGURE 7.

Correlation maps of the polar map segments between the predicted and the ground-truth full-view NAC and AC SPECT images of the 150 testing patient studies. The top red dash box and the bottom blue dash box show the NAC and AC SPECT images respectively. The red dash line in each figure represents the identity line (y = x). The distributions of correlation points in CUSIP deviate away from the identity line. The correlation points in DuDoSS concentrate most densely along the identity line. The correlation coefficients (Corr. Coef.) and coefficients of determination (R²) are shown at top left side of each plot.

Figure 8 displays the Bland-Altman plots of segment PE between the predicted and ground-truth full-view NAC and AC SPECT images from the 150 patient studies tested. In the polar maps of both NAC and AC images, the PE distributions of CUSIP were obviously lower than 0, leading to higher segment-wise errors. The PE distributions of Sparse-View Baseline were more dispersed than other testing groups. In contrast, the PE distributions of DuDoSS concentrated more densely around 0, showing lower quantification errors than other groups.

FIGURE 8.

Bland-Altman plots of segment PE between the predicted and the ground-truth full-view NAC and AC SPECT images of the 150 testing patient studies. In each plot, the mean errors are denoted with blue solid lines, and the 97.5% confidence interval (±1.96 standard deviations) are denoted as green dash lines. In both NAC and AC images, the errors of CUSIP obviously deviate from the center line y = 0, which leads to much higher absolute errors than other groups. In contrast, the error of DuDoSS concentrates more densely along y = 0, showing lower segment-wise errors than other groups.

Table 6 lists the segment-wise quantitative evaluations of the polar maps in terms of the APE from the 150 patient studies used for testing. CUSIP and CUSIP-DuRDN showed the highest errors. Direct Img2Img showed slightly better performance than Direct Sino2Sino, which was consistent with the SPECT images shown in Figure 4 and polar maps shown in Figure 6. Our DuDoSS yielded the most accurate polar maps compared with other testing groups. The significant p-values further showed that DuDoSS were statistically more accurate than the other testing groups.

TABLE 6.

Quantitative evaluations of the polar map segments of the 150 testing patients.

Testing Groups	NAC SPECT Images		AC SPECT Images
	APE (×10−2)	P-valuea	APE (×10−2)	P-valuea
Sparse-View Baseline	5.45 ± 4.35	–	5.19 ± 4.58	–
CUSIP	12.23 ± 4.46	–	11.35 ± 4.52	–
CUSIP-DuRDN	6.41 ± 4.23	< 0.001*	5.97 ± 4.15	< 0.001*
Direct Sino2Sino	4.79 ± 3.69	< 0.001*	4.46 ± 3.58	< 0.001*
Direct Img2Img	4.34 ± 3.50	< 0.001*	3.95 ± 3.21	< 0.001*
DuDoSS (proposed)	3.92 ± 3.20	< 0.001*	3.87 ± 3.23	0.023*

^aTwo-tailed paired t-test of APE between the current and previous group.

^*Refers to significant difference with a significance level of 0.05.

4. DISCUSSION

We have established a novel deep-learning-based algorithm DuDoSS to generate synthetic full-view projections from sparsely sampled projections of cardiac SPECT. The prior image predicted in the image domain was forward-projected and utilized as guidance for the generation of synthetic full-view projections in the sinogram domain. For data consistency, the S_{prior−combine} was combined with Angle 1 of the S_sparse and Angles 2–4 of the S_prior. The S_prior provided a prior coarse estimation of Angles 2–4 in the target sinogram S_full. Thus, the S_{prior−combine} contained the information of both the ground-truth Angle 1 and the prior estimation of Angles 2–4. The prior estimation of Angles 2–4 enabled the input S_{prior−combine} to be closer to the target S_full, and thus enabled the SinoNet to be easier to predict a more accurate synthetic sinogram. In contrast, it was more challenging for the Direct Sino2Sino to estimate the S_full since the input of Direct Sino2Sino contains only zero values at Angles 2–4 and thus was further away from the target S_full. The synthetic projections generated with DuDoSS were the most consistent with the ground-truth full-view projections compared to the other groups. The CUSIP approach predicted the projections in Angles 2, 3, and 4 separately using three separate neural networks. In this way, the inter-angle spatial information of image volumes was not fully incorporated into the networks. In DuDoSS, Angles 1, 2, 3, and 4 were all concatenated into the dimension of 64×64×60. Thus, the inter-angle spatial information of Angles 2, 3, and 4 was fully incorporated, which yielded a higher prediction accuracy. If the proposed DuDoSS are deployed in clinical practice, theoretically the SPECT scanning time can be reduced to about only 25% of that using the conventional full-view scanning since only one fourth of the angles are used. This scanning time can be potentially further reduced if sparser projections are scanned. In addition, the time of generating synthetic projections using DuDoSS is neglectable, less than 100 ms for each patient. Even though the total scanning time can be largely reduced, extensive validation of DuDoSS in real clinical scenario should be performed before this technique is translated into clinical applications.

A good performance was previously reported for CUSIP in the sinogram synthesis of whole-body ¹⁷⁷Lu SPECT³⁷. However, CUSIP did not yield favorable results for ^99mTc-tetrofosmin cardiac SPECT images in our study. The observed inconsistency in performance of CUSIP might be related to difference in the whole-body and cardiac imaging protocols, tracer types, data noise level, etc.

It can be noticed that the MLEM algorithm is derived based on Poisson distributed data,^{51, 52} but the synthetic projections in our study are not strictly Poisson distributed. The MLEM algorithm can sometimes be used when the data is not strictly Poisson distributed.⁵³ In addition, the proposed DuDoSS method in this paper focuses on synthetic projection generations instead of image reconstructions. Based on the properties of the synthetic projections, more appropriate algorithms, such as Maximum a Posteriori (MAP)⁵⁴ and Penalized Weighted Least-Squared (PWLS),⁵⁵ could be applied depending on user’s preference.

However, using MLEM reconstruction on non-Poisson synthetic data could still be a major limitation of this study. Investigating other networks and loss functions to maintain Poisson distribution should be pursued in future studies. For example, adding a convolutional module, such as the variational autoencoder (VAE),⁵⁶ could be a promising solution to amend the statistical properties of the synthetic sinograms. The statistical properties of the synthetic sinograms can be extracted and encoded at the bottleneck latent space of VAE, which can be then modified to satisfy the conditions of the Poisson distribution. This might address the non-Poisson issue and be the next promising research direction to explore.

The complexity of DuDoSS compared with other approaches cannot be ignored. Two neural networks were concatenated in an end-to-end manner to enable the information transition from the image domain to the sinogram domain. Although the total training time of DuDoSS was shorter than CUSIP-DuRDN, implementing DuDoSS still consumed more memories. How to simplify the overall architectures of DuDoSS while keeping the original performance will be a meaningful algorithm-optimization topic to explore in the future. A potential solution is to reduce the number of convolutional layers in DuRDN or replace the DuRDN with other simpler but efficient modules like ResNet.³² Another solution could be based on the weight-shared strategy.⁵⁷ The weights of some structures in ImgNet and SinoNet that have similar functions can be shared with each other. For example, the weights of the input encoding layer of ImgNet can be reused in the SinoNet to reduce the total amount of parameters in the whole framework.

The image noise level was another important factor in this study. In Figure 3, the noise levels of the synthetic projections were lower than the ground-truth projections. A style-transferring convolutional module could be incorporated into the overall workflow to adjust the noise level to make the noise level of the synthetic projections more consistent. This might be a promising research direction to explore in the future. In addition, incorporating the statistical properties of the synthetic projections could be another promising research direction to further improve the prediction accuracy. A potential solution is developing additional convolutional modules to extract and represent the Poisson statistical properties of the synthetic sinograms. Then, the extracted statistical properties can be further regularized by KL-divergence or related loss functions, to further improve the network performance.

5. CONCLUSIONS

Our proposed DuDoSS approach was demonstrated to be an effective approach to generate accurate synthetic projections from sparsely-sampled projections of cardiac SPECT. The synthetic projections by DuDoSS were the most consistent with the ground-truth full-view projections when compared to previous approaches. The reconstructed NAC and AC SPECT images using the synthetic projections generated by DuDoSS showed the lowest voxel-wise and segment-wise errors. DuDoSS demonstrated good performance in the sparse-view cardiac SPECT reconstruction and can potentially enable fast data acquisition of cardiac SPECT.

DATA AVAILABILITY STATEMENTS

The data that supports the findings of this study area available from the corresponding author upon reasonable request and approval of Yale University.