Multi- and Hyperspectral Imaging (HSI) are characterized by the discrepancy between the dimensionality of hyperspectral image and video data and the dimensionality of the spectral detectors. This issue has been addressed by various schemes, including the Snapshot Mosaic Multispectral Imaging architecture, where each pixel (or group of pixels) is associated with a single spectral band. An unavoidable side effect of this design is the hard trade-off between spatial and spectral resolution. In this work, we propose a formal approach for overcoming this tradeoff by formulating the problem of full resolution recovery as a low rank Matrix Completion problem. Furthermore, we extend the traditional formulation of Matrix Completion by introducing non-negativity constraints during the recovery process, thus significantly enhancing the reconstruction quality. Experimental results suggest that the Non-Negative Matrix Completion (NN-MC) framework is capable of estimating a high spatial and spectral resolution hypercube from a single exposure, surpassing state-of- the-art schemes like the nearest-neighbors as well as the unconstrained Matrix Completion techniques.