Medical image reconstruction methods based on deep learning have recently demonstrated powerful performance in photoacoustic tomography (PAT) from limited-view and sparse data. However, because most of these methods must utilize conventional linear reconstruction methods to implement signal-to-image transformations, their performance is restricted. In this paper, we propose a novel deep learning reconstruction approach that integrates appropriate data pre-processing and training strategies. The Feature Projection Network (FPnet) presented herein is designed to learn this signal-to-image transformation through data-driven learning rather than through direct use of linear reconstruction. To further improve reconstruction results, our method integrates an image post-processing network (U-net). Experiments show that the proposed method can achieve high reconstruction quality from limited-view data with sparse measurements. When employing GPU acceleration, this method can achieve a reconstruction speed of 15 frames per second.