Portable MRI scanners that operate at very low magnetic fields are increasingly being deployed in clinical settings. However, the intrinsic low signal-to-noise (SNR) ratio of these low-field MRI scanners often necessitates many signal averages, and therefore excessively long acquisition times. Here we propose to improve SNR through optimized k-space undersampling and Compressed Sensing reconstruction. We demonstrate this approach for 6.5 mT ultra-low-field MRI using: (1) retrospective-subsampling experiments with 2x to 4x acceleration; (2) prospectively-subsampled data acquired from a human brain phantom with a 6.5mT MRI. The results exhibit a higher SNR than the traditional averaging method, without increasing scan time.