Fourier Magnetic Imaging with Nanoscale Resolution and Compressed   Sensing Speed-up using Electronic Spins in Diamond
  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. 
K. Arai, C. Belthangady, H. Zhang, N. Bar-Gill, S. J. DeVience, P.   Cappellaro, A. Yacoby and R. L. Walsworth
cond-mat.mes-hall quant-ph