With the introduction of very dense sensor arrays in ultrasound (US) imaging, data transfer rate and data storage became a bottleneck in ultrasound system design. To reduce the amount of sampled channel data, we propose to use a low-rank and joint-sparse model to represent US signals and exploit the correlations between adjacent receiving channels. Results show that the proposed method is adapted to the ultrasound signals and can recover high quality image approximations from as low as 10% of the samples.