A technique is described to localize MR signals from a target volume using nonlinear pulsed magnetic fields and spatial encoding trajectories designed using local k-space theory. The concept of local k-space is outlined theoretically, and this principle is applied to simulated phantom and cardiac MRI data in the presence of surface and quadrupolar gradient coil phase modulation. Phantom and in vivo human brain images are obtained using a custom, high-performance quadrupolar gradient coil integrated with a whole-body 3-T MRI system to demonstrate target localization using three-dimensional T-weighted spoiled gradient echo, two-dimensional segmented, multiple gradient encoded spin echo, and three-dimensional balanced steady-state free precession acquisitions. This method may provide a practical alternative to selective radiofrequency excitation at ultra-high-field, particularly for steady-state applications where repetition time (TR) must be minimized and when the amount of energy deposited in human tissues is prohibitive. There are several limitations to the approach including the spatial variation in resolution, high frequency aliasing artifacts, and spatial variation in echo times and contrast. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.