Positron emission tomography (PET) imaging encounters the obstacle of partial volume effects, arising from its limited intrinsic resolution, giving rise to (I) considerable bias, particularly for structures comparable in size to the point spread function (PSF) of the system; and (II) blurred image edges and blending of textures along the borders. We set out to build a deep learning-based framework for predicting partial volume corrected full-dose (FD + PVC) images from either standard or low-dose (LD) PET images without requiring any anatomical data in order to provide a joint solution for partial volume correction and de-noise LD PET images. We trained a modified encoder-decoder U-Net network with standard of care or LD PET images as the input and FD + PVC images by six different PVC methods as the target. These six PVC approaches include geometric transfer matrix (GTM), multi-target correction (MTC), region-based voxel-wise correction (RBV), iterative Yang (IY), reblurred Van-Cittert (RVC), and Richardson-Lucy (RL). The proposed models were evaluated using standard criteria, such as peak signal-to-noise ratio (PSNR), root mean squared error (RMSE), structural similarity index (SSIM), relative bias, and absolute relative bias. Different levels of error were observed for these partial volume correction methods, which were relatively smaller for GTM with a SSIM of 0.63 for LD and 0.29 for FD, IY with an SSIM of 0.63 for LD and 0.67 for FD, RBV with an SSIM of 0.57 for LD and 0.65 for FD, and RVC with an SSIM of 0.89 for LD and 0.94 for FD PVC approaches. However, large quantitative errors were observed for multi-target MTC with an RMSE of 2.71 for LD and 2.45 for FD and RL with an RMSE of 5 for LD and 3.27 for FD PVC approaches. We found that the proposed framework could effectively perform joint de-noising and partial volume correction for PET images with LD and FD input PET data (LD vs. FD). When no magnetic resonance imaging (MRI) images are available, the developed deep learning models could be used for partial volume correction on LD or standard PET-computed tomography (PET-CT) scans as an image quality enhancement technique.