British physicist Peter Mansfield developed a mathematical technique that would allow NMR scans to take seconds rather than hours and produce clearer images than the technique Paul Lauterbur developed in 1973.
Mansfield showed how gradients in the magnetic field could be mathematically analysed, which made it possible to develop a useful nuclear magnetic resonance imaging technique. Mansfield also showed how extremely fast imaging could be achievable. This became technically possible a decade later.
P Mansfield and A A Maudsley, Medical imaging by NMR, Brit. J. Radiol. 50 (1977) 188.
P Mansfield, Multi-planar imaging formation using NMR spin echoes J. Physics C. Solid State Phys. 10 (1977) L55–L58.
The references from Mansfield's Nobel Lecture. You can also watch a 64 minute video of Mansfield delivering his lecture at this link.