This paper is part of the challenge on plane wave imaging in medical ultrasound , organized during the IEEE International Ultrasonics Symposium 2016 in Tours (France). Herein, we address beamforming in ultrasound imaging, by formulating it, for each image depth, as an inverse problem solved using Laplacian prior through Basis Pursuit (BP). This approach was evaluated for the four different categories proposed for the competition, using 1, 11, 75 plane waves, and for the best ultrasound image quality using the lowest number of steered plane waves. The proposed method results in considerable improvement in spatial resolution and contrast compared with DAS method proposed in the challenge.