Abstract: The invention relates to nuclear magnetic resonance (NMR) imaging and spectroscopy in which a combination of pulsed radio frequency fields and gradient magnetic fields, called pulse sequences, are used to acquire data from a sample's nuclear spins. Using the principles of the invention, these fields are manipulated so as to yield data points that cover a multidimensional space in a regular fashion. Information is then reconstructed from this data by performing an inverse discrete Fourier Transform (IDFT) on the data set. Many varieties of pulse sequences can be used, such as spinwarp imaging, half-Fourier techniques, echo-planar techniques, and chemical shift imaging. The invention may be used for two, three or four-dimensional studies where the dimensions may be any combination of the three spatial dimensions and the signal frequency. In two dimensions, hexagonal sampling patterns are the most efficient, providing an efficiency gain of 13.4%.