This research addresses the problem of acquiring a time series of magnetic resonance images with both high spatial and temporal resolutions. Specifically, we systematically investigate the advantages and limitations of reduced-encoding imaging using a priori constraints. This study reveals that if the available a priori information is a reference image, direct use of this information to 'optimize' data acquisition using the existing wavelet transform or singular value decomposition schemes can undermine the capability to detect new image features. However, proper incorporation of the a priori information in the image reconstruction step can significantly reduce the resolution loss associated with reduced-encoding. For Fourier encoded data, we have shown that the Generalized-Series (GS) model is an effective mathematical framework for carrying out the constrained reconstruction step. Several techniques are proposed in this dissertation to improve the basis functions of the GS model by introducing dynamic information. The two reference reduced-encoding imaging by generalized-series reconstruction (TRIGR) method suppresses background information through the use of a second high resolution reference image. A second technique injects information from the dynamic data into the GS basis functions, as opposed to deriving them solely from the reference information. These techniques allow the GS basis functions to more accurately represent the areas of dynamic change. Finally, motion that occurs between the acquisition of the reference and dynamic data sets can render the reference information useless as a constraint for image reconstruction. A motion compensation method is proposed which uses a similarity norm to accurately detect the motion in spite of contrast changes and the low resolution nature of the dynamic data.