Reduced-encoding MRI has been used in a wide variety of MR applications where temporal resolution is critical. Although the Generalized Series model (with basis functions constructed from a reference image) allows the reconstruction of high-resolution dynamic images from a small number of encodings, the ability of the model to capture localized dynamic features is limited by the model order, which in the past has been set equal to the number of encodings acquired. This paper extends this model by incorporating higher frequency terms, which allows for a sharper reconstruction of new localized features. Since the series coefficients of the higher-order model are underdetermined by the data collected, two important issues arise which are addressed in this paper: the definition of an appropriate regularization criterion and the solution of the corresponding optimization problem. Results from simulated as well as biological data are also provided to demonstrate the properties of this model.