Ultrafast ultrasound (US) imaging is a pioneering imaging modality that achieves higher frame rates than traditional US imaging, enabling the visualization and analysis of fast dynamics in tissues and flows. Nevertheless, images resulting from this technique suffer from a low-quality level. Recently, convolutional neural networks (CNN) have demonstrated great potential for reducing image artifacts and recovering speckle patterns without compromising the frame rate. As yet, CNNs have been mostly trained on large datasets of simulated or in vitro  phantom images, but their performances on in vivo images remains suboptimal. In the current study, we present a method to enhance the image quality of single unfocused acquisitions by relying on a CNN. We introduce a training loss function that accounts for the high dynamic range of the radio frequency data and uses the Kullback–Leibler (KL) divergence to preserve the probability distributions of the echogenicity values. We conduct an extensive performance analysis of our approach using a new large in vivo dataset of 20,000 images. The predicted images are compared qualitatively to the target images obtained from the coherent compounding of 87 plane waves (PW). The structural similarity index measure, peak signal-to-noise ratio and KL divergence are used to quantitatively analyze the performance of our method. Our results demonstrate significant improvements in image quality of single PW acquisitions, highly reducing artifacts.