This work presents a novel method for macromolecule mapping and quantification. The proposed method integrates an FID-based MRSI acquisition with a generalized series (GS) model based extrapolation scheme. The FID acquisition allows for the use of ultrashort echoes and short repetition times for fast imaging with improved SNR efficiency. The GS model effectively makes use of the spectral priors from single voxel spectroscopy and allows for reformulating the back-extrapolation of metabolite signals as a linear problem (in contrast to conventional nonlinear methods). Results from in vivo experiments demonstrate that MM signals estimated by the proposed method are consistent with an inversion recovery based method and lead to better metabolite quantification.