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In PET, the amount of relative (signal-dependent) noise present in different body regions can be significantly different and is inherently related to the number of counts present in that region. The number of counts in a region depends, in principle and among other factors, on the total administered activity, scanner sensitivity, image acquisition duration, radiopharmaceutical tracer uptake in the region, and patient local body morphometry surrounding the region. In theory, less amount of denoising operations is needed to denoise a high-count (low relative noise) image than images a low-count (high relative noise) image, and vice versa. The current deep-learning-based methods for PET image denoising are predominantly trained on image appearance only and have no special treatment for images of different noise levels. Our hypothesis is that by explicitly providing the local relative noise level of the input image to a deep convolutional neural network (DCNN), the DCNN can outperform itself trained on image appearance only. To this end, we propose a noise-level-aware framework denoising framework that allows embedding of local noise level into a DCNN. The proposed is trained and tested on 30 and 15 patient PET images acquired on a GE Discovery MI PET/CT system. Our experiments showed that the increases in both PSNR and SSIM from our backbone network with relative noise level embedding (NLE) versus the same network without NLE were statistically significant with p<0.001, and the proposed method significantly outperformed a strong baseline method by a large margin.