Continuous glucose monitoring (CGM) of patients with diabetes allows the effective management of the disease and reduces the risk of hypoglycemic or hyperglycemic episodes. Towards this goal, the development of reliable CGM models is essential for representing the corresponding signals and interpreting them with respect to factors and outcomes of interest. We propose a sparse decomposition model to approximate CGM time-series as a linear combination of a small set of exemplar atoms, appropriately designed through parametric functions to capture the main fluctuations of the CGM signal. Sparse decomposition is performed through the orthogonal matching pursuit (OMP). Results indicate that the proposed model provides 0.1 relative reconstruction error with 0.8 compression rate on a publicly available dataset containing 25 patients diagnosed with Type 1 diabetes. The atoms selected from the OMP procedure can be further interpreted in relation to the clinically meaningful components of the CGM signal (e.g. glucose spikes, hypoglycemic episodes, etc.