Deep Image Prior (DIP) is an unsupervised way of denoising images with a neural network, trained only using the noisy image. DIP is currently used in Positron Emission Tomography (PET), embedded in the PET reconstruction or directly for PET reconstruction. The original authors used a U-Net architecture with skip connections (SC) and random noise as input. A slightly modified U-Net is usually used in PET, especially with an anatomical image replacing the random input. In this work, we studied the impact of the choice of the input image with the presence or absence of SC. We considered the DIP embedded as a constraint into the PET reconstruction using the DIP Nested ADMM (DNA) and the DIPrecon algorithms. Results demonstrated that anatomical mismatches or noise coming from the chosen input may appear in output images using a network with too many SC, whereas few SC led to distorted regions. An intermediate setting where the anatomical image is used as an input only for the initialization of the network, and then replaced by random noise within the iterations, achieved the best results without mismatch artifacts, and appeared less sensitive with respect to the number of SC.