Photoacoustic tomography (PAT) is an emerging and effective imaging technique, which offers high spatial resolution with high contrast. In particular, the acquired data is incomplete due to geometrical limitations or accelerating data acquisition by undersampling technology, thus some artifacts will be presented in the reconstructed image. To deal with limited-view PAT, we introduce a [Formula: see text] regularization scheme into PAT and propose a three-stage method. We first use the gradient descent method to obtain an initial solution, then project it onto a constrain set, and finally a proximal mapping scheme is used to further improve the reconstruction quality. Our simulation experiments on homogeneous medium are utilized to validate the effectiveness of the proposed method, and a discussion on the parameters of the proposed method is given. The experimental results reveal that the proposed method outperforms other classical methods, and it can further improve the reconstruction quality in terms of suppressing the noise and artifacts, and preserving the edge.