A new technique for estimating postprandial glucose flux profiles without the use of glucose tracers is proposed. A sparse vector space representation is first found for the space of plausible glucose flux profiles using sparse encoding. A Lasso formulation is then used to estimate the glucose fluxes that combines (1) known patient model parameters; (2) the vector space of plausible glucose flux profiles; (3) continuous glucose monitor measurements taken during the meal; (4) amount of insulin injected; (5) amount of meal carbohydrates; and (6) an estimate of the initial conditions. Three glucose fluxes are then estimated, namely; glucose rate of appearance from the intestine; endogenous glucose production from the liver; insulin dependent glucose utilization; and other important state variables. The simulation results show that the technique is capable of estimating the glucose fluxes with high accuracy, even for complex meal scenarios. The experimental results indicate that the technique is capable of reproducing the triple tracer measurements for three T1DM undergoing the triple tracer protocol while estimating the missing measurements for a certain model parameter selection.