Photoacoustic imaging is an emerging imaging modality that is based upon the photoacoustic effect. In photoacoustic tomography (PAT), the induced acoustic pressure waves are measured by an array of detectors and used to reconstruct an image of the initial pressure distribution. A common challenge faced in PAT is that the measured acoustic waves can only be sparsely sampled. Reconstructing sparsely sampled data using standard methods results in severe artifacts that obscure information within the image. We propose a modified convolutional neural network (CNN) architecture termed fully dense UNet (FD-UNet) for removing artifacts from two-dimensional PAT images reconstructed from sparse data and compare the proposed CNN with the standard UNet in terms of reconstructed image quality.