Low-dose PET offers a valuable means of minimizing radiation exposure in PET imaging. However, the prevalent practice of employing additional CT scans for generating attenuation maps (u-map) for PET attenuation correction significantly elevates radiation doses. To address this concern and further mitigate radiation exposure in low-dose PET exams, we propose POUR-Net - an innovative population-prior-aided over-under-representation network that aims for high-quality attenuation map generation from low-dose PET. First, POUR-Net incorporates an over-under-representation network (OUR-Net) to facilitate efficient feature extraction, encompassing both low-resolution abstracted and fine-detail features, for assisting deep generation on the full-resolution level. Second, complementing OUR-Net, a population prior generation machine (PPGM) utilizing a comprehensive CT-derived u-map dataset, provides additional prior information to aid OUR-Net generation. The integration of OUR-Net and PPGM within a cascade framework enables iterative refinement of $\mu$-map generation, resulting in the production of high-quality $\mu$-maps. Experimental results underscore the effectiveness of POUR-Net, showing it as a promising solution for accurate CT-free low-count PET attenuation correction, which also surpasses the performance of previous baseline methods.
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