List-Mode PET Image Reconstruction Using Dykstra-Like Splitting

To converge the block iterative method in image reconstruction for positron emission tomography (PET), careful control of relaxation parameters is required, which is a challenging task. The automatic determination of relaxation parameters for list-mode reconstructions also remains challenging. Therefore, a different approach than controlling relaxation parameters would be desired by list-mode PET reconstruction. In this study, we propose a list-mode maximum likelihood Dykstra-like splitting PET reconstruction (LM-MLDS). LM-MLDS converges the list-mode block iterative method by adding the distance from an initial image as a penalty term into an objective function. LM-MLDS takes a two-step approach because its performance depends on the quality of the initial image. The first step uses a uniform image as the initial image, and then the second step uses a reconstructed image after one main iteration as the initial image. We evaluated LM-MLDS using simulation and clinical data. LM-MLDS provided a higher peak signal-to-noise ratio and suppressed an oscillation of tradeoff curves between noise and contrast than the other block iterative methods. In a clinical study, LM-MLDS removed the false hotspots at the edge of the axial field of view and improved the image quality of slices covering the top of the head to the cerebellum. LM-MLDS showed different noise properties than the other methods due to Gaussian denoising induced by the proximity operator. The list-mode proximal splitting PET reconstruction is useful not only for optimizing nondifferentiable functions such as total variation but also for converging block iterative methods without controlling relaxation parameters.

List-Mode PET Image Reconstruction Using Deep Image Prior

List-mode positron emission tomography (PET) image reconstruction is an important tool for PET scanners with many lines-of-response (LORs) and additional information such as time-of-flight and depth-of-interaction. Deep learning is one possible solution to enhance the quality of PET image reconstruction. However, the application of deep learning techniques to list-mode PET image reconstruction have not been progressed because list data is a sequence of bit codes and unsuitable for processing by convolutional neural networks (CNN). In this study, we propose a novel list-mode PET image reconstruction method using an unsupervised CNN called deep image prior (DIP) and a framework of alternating direction method of multipliers. The proposed list-mode DIP reconstruction (LM-DIPRecon) method alternatively iterates regularized list-mode dynamic row action maximum likelihood algorithm (LM-DRAMA) and magnetic resonance imaging conditioned DIP (MR-DIP). We evaluated LM-DIPRecon using both simulation and clinical data, and it achieved sharper images and better tradeoff curves between contrast and noise than the LM-DRAMA and MR-DIP. These results indicated that the LM-DIPRecon is useful for quantitative PET imaging with limited events. In addition, as list data has finer temporal information than dynamic sinograms, list-mode deep image prior reconstruction is expected to be useful for 4D PET imaging and motion correction.

Anatomical-Guided Attention Enhances Unsupervised PET Image Denoising Performance

Although supervised convolutional neural networks (CNNs) often outperform conventional alternatives for denoising positron emission tomography (PET) images, they require many low- and high-quality reference PET image pairs. Herein, we propose an unsupervised 3D PET image denoising method based on an anatomical information-guided attention mechanism. The proposed magnetic resonance-guided deep decoder (MR-GDD) utilizes the spatial details and semantic features of MR-guidance image more effectively by introducing encoder-decoder and deep decoder subnetworks. Moreover, the specific shapes and patterns of the guidance image do not affect the denoised PET image, because the guidance image is input to the network through an attention gate. In a Monte Carlo simulation of [$^{18}$F]fluoro-2-deoxy-D-glucose (FDG), the proposed method achieved the highest peak signal-to-noise ratio and structural similarity (27.92 $\pm$ 0.44 dB/0.886 $\pm$ 0.007), as compared with Gaussian filtering (26.68 $\pm$ 0.10 dB/0.807 $\pm$ 0.004), image guided filtering (27.40 $\pm$ 0.11 dB/0.849 $\pm$ 0.003), deep image prior (DIP) (24.22 $\pm$ 0.43 dB/0.737 $\pm$ 0.017), and MR-DIP (27.65 $\pm$ 0.42 dB/0.879 $\pm$ 0.007). Furthermore, we experimentally visualized the behavior of the optimization process, which is often unknown in unsupervised CNN-based restoration problems. For preclinical (using [$^{18}$F]FDG and [$^{11}$C]raclopride) and clinical (using [$^{18}$F]florbetapir) studies, the proposed method demonstrates state-of-the-art denoising performance while retaining spatial resolution and quantitative accuracy, despite using a common network architecture for various noisy PET images with 1/10th of the full counts. These results suggest that the proposed MR-GDD can reduce PET scan times and PET tracer doses considerably without impacting patients.