Respiratory motion is one of the main sources of motion artifacts in positron emission tomography (PET) imaging. The emission image and patient motion can be estimated simultaneously from respiratory gated data through a joint estimation framework. However, conventional motion estimation methods based on registration of a pair of images are sensitive to noise. The goal of this study is to develop a robust joint estimation method that incorporates a deep learning (DL)-based image registration approach for motion estimation. We propose a joint estimation framework by incorporating a learned image registration network into a regularized PET image reconstruction. The joint estimation was formulated as a constrained optimization problem with moving gated images related to a fixed image via the deep neural network. The constrained optimization problem is solved by the alternating direction method of multipliers (ADMM) algorithm. The effectiveness of the algorithm was demonstrated using simulated and real data. We compared the proposed DL-ADMM joint estimation algorithm with a monotonic iterative joint estimation. Motion compensated reconstructions using pre-calculated deformation fields by DL-based (DL-MC recon) and iterative (iterative-MC recon) image registration were also included for comparison. Our simulation study shows that the proposed DL-ADMM joint estimation method reduces bias compared to the ungated image without increasing noise and outperforms the competing methods. In the real data study, our proposed method also generated higher lesion contrast and sharper liver boundaries compared to the ungated image and had lower noise than the reference gated image.

Artifacts caused by patient breathing and movement during PET data acquisition affect image quality. Respiratory gating is commonly used to gate the list-mode PET data into multiple bins over a respiratory cycle. Non-rigid registration of respiratory-gated PET images can reduce motion artifacts and preserve count statistics, but it is time consuming. In this work, we propose an unsupervised non-rigid image registration framework using deep learning for motion correction. Our network uses a differentiable spatial transformer layer to warp the moving image to the fixed image and uses a stacked structure for deformation field refinement. Estimated deformation fields were incorporated into an iterative image reconstruction algorithm to perform motion compensated PET image reconstruction. We validated the proposed method using simulation and clinical data and implemented an iterative image registration approach for comparison. Motion compensated reconstructions were compared with ungated images. Our simulation study showed that the motion compensated methods can generate images with sharp boundaries and reveal more details in the heart region compared with the ungated image. The resulting normalized root mean square error (NRMS) was 24.3 ± 1.7% for the deep learning based motion correction, 31.1 ± 1.4% for the iterative registration based motion correction, and 41.9 ± 2.0% for ungated reconstruction. The proposed deep learning based motion correction reduced the bias compared with the ungated image without increasing the noise level and outperformed the iterative registration based method. In the real data study, both motion compensated images provided higher lesion contrast and sharper liver boundaries than the ungated image and had lower noise than the reference gate image. The contrast of the proposed method based on the deep neural network was higher than the ungated image and iterative registration method at any matched noise level.

We describe a method for computing a continuous time estimate of tracer density using list-mode positron emission tomography data. The rate function in each voxel is modeled as an inhomogeneous Poisson process whose rate function can be represented using a cubic B-spline basis. The rate functions are estimated by maximizing the likelihood of the arrival times of detected photon pairs over the control vertices of the spline, modified by quadratic spatial and temporal smoothness penalties and a penalty term to enforce nonnegativity. Randoms rate functions are estimated by assuming independence between the spatial and temporal randoms distributions. Similarly, scatter rate functions are estimated by assuming spatiotemporal independence and that the temporal distribution of the scatter is proportional to the temporal distribution of the trues. A quantitative evaluation was performed using simulated data and the method is also demonstrated in a human study using 11C-raclopride.

Background

Physiological motion, such as respiratory motion, has become a limiting factor in the spatial resolution of positron emission tomography (PET) imaging as the resolution of PET detectors continue to improve. Motion-induced misregistration between PET and CT images can also cause attenuation correction artifacts. Respiratory gating can be used to freeze the motion and to reduce motion induced artifacts.

Purpose

In this study, we propose a robust data-driven approach using an unsupervised deep clustering network that employs an autoencoder (AE) to extract latent features for respiratory gating.

Methods

We first divide list-mode PET data into short-time frames. The short-time frame images are reconstructed without attenuation, scatter, or randoms correction to avoid attenuation mismatch artifacts and to reduce image reconstruction time. The deep AE is then trained using reconstructed short-time frame images to extract latent features for respiratory gating. No additional data are required for the AE training. K-means clustering is subsequently used to perform respiratory gating based on the latent features extracted by the deep AE. The effectiveness of our proposed Deep Clustering method was evaluated using physical phantom and real patient datasets. The performance was compared against phase gating based on an external signal (External) and image based principal component analysis (PCA) with K-means clustering (Image PCA).

Results

The proposed method produced gated images with higher contrast and sharper myocardium boundaries than those obtained using the External gating method and Image PCA. Quantitatively, the gated images generated by the proposed Deep Clustering method showed larger center of mass (COM) displacement and higher lesion contrast than those obtained using the other two methods.

Conclusions

The effectiveness of our proposed method was validated using physical phantom and real patient data. The results showed our proposed framework could provide superior gating than the conventional External method and Image PCA.

Purpose

The developments of PET/CT and PET/MR scanners provide opportunities for improving PET image quality by using anatomical information. In this paper, we propose a novel co-learning three-dimensional (3D) convolutional neural network (CNN) to extract modality-specific features from PET/CT image pairs and integrate complementary features into an iterative reconstruction framework to improve PET image reconstruction.

Methods

We used a pretrained deep neural network to represent PET images. The network was trained using low-count PET and CT image pairs as inputs and high-count PET images as labels. This network was then incorporated into a constrained maximum likelihood framework to regularize PET image reconstruction. Two different network structures were investigated for the integration of anatomical information from CT images. One was a multichannel CNN, which treated PET and CT volumes as separate channels of the input. The other one was multibranch CNN, which implemented separate encoders for PET and CT images to extract latent features and fed the combined latent features into a decoder. Using computer-based Monte Carlo simulations and two real patient datasets, the proposed method has been compared with existing methods, including the maximum likelihood expectation maximization (MLEM) reconstruction, a kernel-based reconstruction and a CNN-based deep penalty method with and without anatomical guidance.

Results

Reconstructed images showed that the proposed constrained ML reconstruction approach produced higher quality images than the competing methods. The tumors in the lung region have higher contrast in the proposed constrained ML reconstruction than in the CNN-based deep penalty reconstruction. The image quality was further improved by incorporating the anatomical information. Moreover, the liver standard deviation was lower in the proposed approach than all the competing methods at a matched lesion contrast.

Conclusions

The supervised co-learning strategy can improve the performance of constrained maximum likelihood reconstruction. Compared with existing techniques, the proposed method produced a better lesion contrast versus background standard deviation trade-off curve, which can potentially improve lesion detection.

Penalized likelihood (PL) reconstruction has demonstrated potential to improve image quality of positron emission tomography (PET) over unregularized ordered-subsets expectation-maximization (OSEM) algorithm. However, selecting proper regularization parameters in PL reconstruction has been challenging due to the lack of ground truth and variation of penalty functions. Here we present a method to choose regularization parameters using a cross-validation log-likelihood (CVLL) function. This new method does not require any knowledge of the true image and is directly applicable to list-mode PET data. We performed statistical analysis of the mean and variance of the CVLL. The results show that the CVLL provides an unbiased estimate of the log-likelihood function calculated using the noise free data. The predicted variance can be used to verify the statistical significance of the difference between CVLL values. The proposed method was validated using simulation studies and also applied to real patient data. The reconstructed images using optimum parameters selected by the proposed method show good image quality visually.

Positron emission tomography (PET) is an ill-posed inverse problem and suffers high noise due to limited number of detected events. Prior information can be used to improve the quality of reconstructed PET images. Deep neural networks have also been applied to regularized image reconstruction. One method is to use a pretrained denoising neural network to represent the PET image and to perform a constrained maximum likelihood estimation. In this work, we propose to use a generative adversarial network (GAN) to further improve the network performance. We also modify the objective function to include a data-matching term on the network input. Experimental studies using computer-based Monte Carlo simulations and real patient datasets demonstrate that the proposed method leads to noticeable improvements over the kernel-based and U-net-based regularization methods in terms of lesion contrast recovery versus background noise trade-offs.