A unified description of NMR imaging, data-collection strategies, and reconstruction

In nuclear magnetic resonance (NMR) imaging by the zeugmatographic methods, there is a common and unified theoretical description. All forms of two-dimensional and three-dimensional imaging involve NMR data which trace various geometric representations, in reciprocal transform space, of the subject's spatially blurred "effective" spin density. The effective density is proportional to the physical density modulated spatially by the several factors of receiver coil (B/I) ratio, rf pulse excitation terms, T1-relaxation terms, and T2-relaxation terms. These factors depend upon the rf pulse sequence and field-gradient modulation sequence,and they may be calculated according to some model or directly measured. From this viewpoint, all different imaging modes appear as variations in data-collection and image-reconstruction strategies. The results are used here to describe slice-oriented polar and Cartesian strategies, three-dimensional Cartesian and two forms of spherical strategies, and multiecho strategies of the "planar-echo" type.