High-spectral resolution imaging provides critical insights into important computer vision tasks such as classification, tracking, and remote sensing. Modern Snapshot Spectral Imaging (SSI) systems directly acquire the entire 3D data-cube through the intelligent combination of spectral filters and detector elements. Partially because of the dramatic reduction in acquisition time, SSI systems exhibit limited spectral resolution, for example, by associating each pixel with a single spectral band in Spectrally Resolvable Detector Arrays. In this paper, we propose a novel machine learning technique aiming to enhance the spectral resolution of imaging systems by exploiting the mathematical framework of Sparse Representations (SR). Our formal approach proposes a systematic way to estimate a high-spectral resolution pixel from a measured low-spectral resolution version by appropriately identifying a sparse representation that can directly generate the highspectral resolution output. We enforce the sparsity constraint by learning a joint space coding dictionary from multiple low and high spectral resolution training data and we demonstrate that one can successfully reconstruct high-spectral resolution images from limited spectral resolution measurements.