AbstractHinshaw's sensitive‐point method and Macovski's post‐filtering localization techniques are analyzed under very general imaging conditions. It is shown that one can obtain an expression for the FID signal induced by all resonating particles at any particular point in the imaged object. Contributors to the signal may have different relaxation behaviors, spin rates, and velocity components. In fact, in the case of flows, different nuclei contribute to the signal at different times during the observation. Localization enables us to impose local assumptions on our model rather than global ones, as is usually done in MRI. Applications to imaging slow and fast flows andin vivospectroscopy are discussed. © 1987 Academic Press,