Filling of incomplete sinograms from sparse PET detector configurations using a residual U-Net

TL;DR

This study addresses the challenge of high detector costs in long axial FOV PET by exploring a sparse chessboard detector configuration and restoring missing sinogram data with a Residual U-Net. The authors create a simulated dataset from MORRIS scans, train a 2D sinogram restoration network, and evaluate performance against 2D interpolation in both sinogram and image domains using SSIM, MAE, and ROI-based metrics, coupled with standard PET reconstruction. The restored sinograms achieve MAE below $2$ counts per pixel and better SSIM/MAE than interpolation, but the approach introduces smoothing that reduces fine image detail and contrast recovery. Overall, this proof-of-concept demonstrates the potential for cost-effective, extended-FOV PET systems aided by deep learning, while outlining clear directions for improving sharpness, generalizability, and integration into clinical workflows.

Abstract

Long axial field-of-view PET scanners offer increased field-of-view and sensitivity compared to traditional PET scanners. However, a significant cost is associated with the densely packed photodetectors required for the extended-coverage systems, limiting clinical utilisation. To mitigate the cost limitations, alternative sparse system configurations have been proposed, allowing an extended field-of-view PET design with detector costs similar to a standard PET system, albeit at the expense of image quality. In this work, we propose a deep sinogram restoration network to fill in the missing sinogram data. Our method utilises a modified Residual U-Net, trained on clinical PET scans from a GE Signa PET/MR, simulating the removal of 50% of the detectors in a chessboard pattern (retaining only 25% of all lines of response). The model successfully recovers missing counts, with a mean absolute error below two events per pixel, outperforming 2D interpolation in both sinogram and reconstructed image domain. Notably, the predicted sinograms exhibit a smoothing effect, leading to reconstructed images lacking sharpness in finer details. Despite these limitations, the model demonstrates a substantial capacity for compensating for the undersampling caused by the sparse detector configuration. This proof-of-concept study suggests that sparse detector configurations, combined with deep learning techniques, offer a viable alternative to conventional PET scanner designs. This approach supports the development of cost-effective, total body PET scanners, allowing a significant step forward in medical imaging technology.

Figures (11)

• Figure 1: Example comparison of a standard compact PET configuration (a) and a sparse PET configuration using a chessboard detector pattern (b). For the sake of resolution, the shown mockup scanners comprise of 15 rings with 128 detector elements each.
• Figure 2: Visualisation of the sinogram distortion due to the sparse PET chessboard configuration. (a) Pixel-wise correlation between the original and distorted sinograms; figure shows random sample of $10^5$ pixels from the different scans (different colours for different scans). The distorted pixels follow two separate distributions (marked by arrows) -- they are either zero (i) or of lower intensity than the original (ii). The ideal fit is illustrated by a solid line, and the overall total fit to the original pixels is illustrated by a dashed line. (b) shows the sinogram distortion pattern with zeroed out pixels in direct planes and cross planes with ring difference $>1$. (c) shows the sinogram distortion pattern with low-intensity pixels in summed cross planes with ring difference 1.
• Figure 3: Architecture of the implemented sinogram restoration network. Each green arrow represents a residual block containing convolution, batch normalisation and rectified linear unit (ReLU) activation, as well as a residual connection. The dotted arrows represent skip connections, and the circled plus signs represent addition of the features from the down-sampling layers with the up-sampling layers. The network down-samples via convolution with stride 2, reducing the spatial dimensions by half, and up-samples using transpose convolution, doubling the spatial dimensions. Two final convolutions layers are used to generate the output. The sinograms are normalised to range $[0:1]$ before input and denormalised by the same factor after output. Finally, the pixels not affected by the removed detectors are copied from the input sinograms and reinstated in the output.
• Figure 4: Visual comparison of 2D sinograms based on the ground truth (Original), the sparse chessboard configuration (Distorted), and predictions from interpolation filling (Interpolated) and from the sinogram restoration network (Restored). The figure includes two different sinogram slices from one scan in the test set. (a) shows a direct plane sinogram slice. (b) shows a summed cross-plane sinogram slice with ring difference 1.
• Figure 5: Pixel-wise correlation between the original sinograms and the predicted sinograms from (a) interpolation and (b) the restoration network. The figure shows a random sample of $10^5$ pixels from the different scans (different colours for different scans). The ideal fit is illustrated by the solid lines, and the overall total fit to the original pixels is illustrated by the dashed lines. The interpolated pixels exhibit traces of the two separate distributions of the distorted pixels with remaining pixels of lower intensity than the original (marked by arrow).