2.5D Nouveau VAE model for 11C-DASB PET image denoising and uncertainty estimation

Introduction: Denoising is a widely used postprocessing technique that can rapidly improve image quality with minimal cost. Recent studies show that deep neural network-based denoising methods have better denoising performance than traditional methods. However, these denoising models are mostly based on determinant models, the uncertainty of which cannot be estimated. Uncertainty estimation is very important for PET image denoising tasks, as the denoising model cannot tell whether it is noise or a small lesion. In this work, we performed PET denoising through the Nouveau variational autoencoder (NVAE) model, which is trained to learn the distribution of the training images instead of the images themselves. Based on NVAE, an uncertainty map can be generated at the same time of denoising.

Methods: The study included 26 ¹¹C-DASB datasets acquired from the HRRT-PET scanner (Siemens Medical Solutions). The administered dose was 577.6±41.0 MBq. The quarter-dose images were generated from the full dose list-mode data and all images were reconstructed by the 3D-OSEM algorithm. In this study, we employed 20 datasets for training, 3 for validation, and the remaining 3 for testing. The schematic plot of the proposed method is shown in Fig. 1. When the 2.5D input was supplied to the pre-trained NVAE model, the model will generate a series of samples according to the learned distribution. From these samples, their mean and variance can be obtained. Compared to the traditional VAE model, the NVAE model included a hierarchical multi-scale structure between the encoder and the generative model. Based on this structure, the model can capture global long-range correlations. In NVAE, the latent variables were partitioned into disjoint groups and parameterized as residual normal distributions. Spectral regularization was used to bound Kullback–Leibler divergence and depthwise convolutions were added in the generative path to increase the receptive field of the network. In this work, the network was implemented in Pytorch 1.9.1, the batch size was 20, the number of training epochs was 200, and the patch size was 3×256×256. Compared to the 5- and 7-slice patches, the 3-slice patch had better performance and lower computation costs.

Results: Fig. 2 showed an axial view of the denoised image from the test PET datasets. We can see that compared to the one sample result, the mean from 500 samples was smoother with higher contrast. Table 1 listed the PSNR and SSIM of the quarter dose image, Unet, NVAE (1 sample), and NVAE mean from 500 samples. The one sample NVAE result (PSNR, 29.22±0.44; SSIM, 0.9174±0.0045) had lower mean(±SD) quantitative scores than Unet (PSNR, 29.72±0.42; SSIM, 0.9175±0.0044). After averaging, NVAE mean result (PSNR, 30.10±0.44; SSIM, 0.9248±0.0040) was better than Unet. The variance map shown in Fig.3 indicated that the NVAE denoised image had high uncertainty in the thalamus.

Conclusions: In this work, we proposed a novel model, NVAE, for ¹¹C-DASB PET image denoising as well as uncertainty quantification. The mean image from NVAE can achieve better results than Unet and the variance image from NVAE can provide the doctor with guidance on the high uncertainty regions.

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