Non-parametric Bayesian deep learning approach for whole-body low-dose PET reconstruction and uncertainty assessment

Positron emission tomography (PET) imaging plays a pivotal role in oncology for the early detection of metastatic tumors and response to therapy assessment due to its high sensitivity compared to anatomical imaging modalities. The balance between image quality and radiation exposure is critical, as reducing the administered dose results in a lower signal-to-noise ratio (SNR) and information loss, which may significantly affect clinical diagnosis. Deep learning (DL) algorithms have recently made significant progress in low-dose (LD) PET reconstruction. Nevertheless, a successful clinical application requires a thorough evaluation of uncertainty to ensure informed clinical judgment. We propose NPB-LDPET, a DL-based non-parametric Bayesian framework for LD PET reconstruction and uncertainty assessment. Our framework utilizes an Adam optimizer with stochastic gradient Langevin dynamics (SGLD) to sample from the underlying posterior distribution. We employed the Ultra-low-dose PET Challenge dataset to assess our framework's performance relative to the Monte Carlo dropout benchmark. We evaluated global reconstruction accuracy utilizing SSIM, PSNR, and NRMSE, local lesion conspicuity using mean absolute error (MAE) and local contrast, and the clinical relevance of uncertainty maps employing correlation between the uncertainty measures and the dose reduction factor (DRF). Our NPB-LDPET reconstruction method exhibits a significantly superior global reconstruction accuracy for various DRFs (paired t-test, $p<0.0001$ , N=10, 631). Moreover, we demonstrate a 21% reduction in MAE (573.54 vs. 723.70, paired t-test, $p<0.0001$ , N=28) and an 8.3% improvement in local lesion contrast (2.077 vs. 1.916, paired t-test, $p<0.0001$ , N=28). Furthermore, our framework exhibits a stronger correlation between the predicted uncertainty 95th percentile score and the DRF ( $r^2=0.9174$ vs. $r^2=0.6144$ , N=10, 631). The proposed framework has the potential to improve clinical decision-making for LD PET imaging by providing a more accurate and informative reconstruction while reducing radiation exposure.