A method is proposed for fast magnetic resonance imaging (MRI) acquisition of targeted specific structures. The method is based on the correlation between the inverse space (k-space) and the real space geometry of the imaged structure. Theoretical and simulation studies were performed with segments of straight and curved vessels. In cases when we are interested for only a segment of a vessel, as example for interventions, these studies show that as small as 1/8 of the whole k-space data is sufficient to reconstruct the interested vessel without compromise in the image quality.