Sensitivity Estimation and Image Reconstruction for Sparse PET with Deep Learning

The use of a sparse crystal setting would reduce the cost of the PET scanner and has advantages such as less RF shielding in PET/MR. It also allows a longer axial field of view (FOV) using the same crystal volume. In this paper, the sensitivities of the coincidence events of PET systems with the sparse crystal configuration, thin crystal setting, and the conventional design using a fixed total crystal volume were analytically estimated. The sinograms of a sparse system (with 50% crystal removed and fixed axial FOV) were simulated using patient data. Reconstruction algorithms were developed by modeling the effects of reduced crystals in the system matrix. A convolutional neural network (CNN) based noise reduction approach was used for post-processing. A total of 14 patient data were included and were truncated to 3 minutes scan for consistency. Leave-one-out cross-validation was used for evaluation purpose. A patch based data input/output was used for model training to increase the number of training samples. Images reconstructed using OSEM followed by Gaussian denoising was also used as a comparison. The percentage summed square difference (SSD) between images of sparse crystal configuration and non-sparse systems were used for quantitative evaluation. When using the same total volume of crystals, the difference of sensitivity at the center of FOV was within 10% among three different settings, with the rank from highest to lowest being the thin detector, sparse detector, and conventional detector. When using the same axial FOV, reconstructed images of the sparse crystal configuration showed increased noise due to reduced sensitivity. The percentage SSD for image processed with the Gaussian filter was 30% on average and was reduced to 16% with CNN on average. The results show with the same amount of crystal, the use of sparse crystal configuration provides a slightly larger sensitivity and much larger axial FOV. CNN processed images was able to partially recover lost image quality due to the removal of certain crystals.