%0 Journal Article %T Fourier Magnetic Imaging with Nanoscale Resolution and Compressed Sensing Speed-up using Electronic Spins in Diamond %A K. Arai %A C. Belthangady %A H. Zhang %A N. Bar-Gill %A S. J. DeVience %A P. Cappellaro %A A. Yacoby %A R. L. Walsworth %J Physics %D 2014 %I arXiv %R 10.1038/nnano.2015.171 %X Optically-detected magnetic resonance using Nitrogen Vacancy (NV) color centres in diamond is a leading modality for nanoscale magnetic field imaging, as it provides single electron spin sensitivity, three-dimensional resolution better than 1 nm, and applicability to a wide range of physical and biological samples under ambient conditions. To date, however, NV-diamond magnetic imaging has been performed using real space techniques, which are either limited by optical diffraction to 250 nm resolution or require slow, point-by-point scanning for nanoscale resolution, e.g., using an atomic force microscope, magnetic tip, or super-resolution optical imaging. Here we introduce an alternative technique of Fourier magnetic imaging using NV-diamond. In analogy with conventional magnetic resonance imaging (MRI), we employ pulsed magnetic field gradients to phase-encode spatial information on NV electronic spins in wavenumber or k-space followed by a fast Fourier transform to yield real-space images with nanoscale resolution, wide field-of-view (FOV), and compressed sensing speed-up. %U http://arxiv.org/abs/1409.2749v1