Sparse arrays offer a promising solution for reducing the data volume required to reconstruct ultrasound images, making them well-suited for portable and wireless devices. However, the quality of images beamformed from a limited number of transducer elements is significantly degraded. This study proposes a deep learning-based inpainting technique to estimate complete radio frequency (RF) signals (before beamforming) from downsampled RF signals obtained using a subset of transducer elements. This approach allows for quality enhancement without the need to beamform images, offering flexibility particularly beneficial for applications such as speed-of-sound estimation algorithms. We introduce a model-based loss function that combines the signal and image domains by incorporating a measurement model associated with image reconstruction. We then compare this loss with another that accounts solely for the RF signal domain. Additionally, we train our network exclusively in the RF image domain, mapping images beamformed from downsampled RF signals to those from complete signals. We compare these approaches qualitatively and quantitatively, with all enhancing image quality. The proposed method with the modelbased loss achieves superior detail and quality metrics. Although trained on downsampled RF signals simulating sparse arrays in reception, all methods-especially our inpainting approach with the model-based loss-demonstrate strong adaptability to ultrafast acquisitions with reduced transducer elements in both transmission and reception. This highlights their potential for reducing the number of transducer elements in ultrasound probes. Furthermore, the proposed method exhibits superior generalization performance when evaluated on a different probe than the one used to acquire the training dataset.