Ultrafast ultrasound imaging, characterized by high frame rates, generates low-quality images. Convolutional neural networks (CNNs) have demonstrated great potential to enhance image quality without compromising the frame rate. However, CNNs have been mostly trained on simulated or phantom images, leading to suboptimal performance on in vivo images. In this study, we present a method to enhance the quality of single plane wave (PW) acquisitions using a CNN trained on in vivo images. Our contribution is twofold. Firstly, we introduce a training loss function that accounts for the high dynamic range of the radio frequency data and uses the Kullback-Leibler divergence to preserve the probability distributions of the echogenicity values. Secondly, we conduct an extensive performance analysis on a large new in vivo dataset of 20,000 images, comparing the predicted images to the target images resulting from the coherent compounding of 87 PWs. Applying a volunteer-based dataset split, the peak signal-to-noise ratio and structural similarity index measure increase, respectively, from 16.466 ± 0.801 dB and 0.105 ± 0.060, calculated between the single PW and target images, to 20.292 ± 0.307 dB and 0.272 ± 0.040, between predicted and target images. Our results demonstrate significant improvements in image quality, effectively reducing artifacts.