6,439 research outputs found
Dynamical Functional Theory for Compressed Sensing
We introduce a theoretical approach for designing generalizations of the
approximate message passing (AMP) algorithm for compressed sensing which are
valid for large observation matrices that are drawn from an invariant random
matrix ensemble. By design, the fixed points of the algorithm obey the
Thouless-Anderson-Palmer (TAP) equations corresponding to the ensemble. Using a
dynamical functional approach we are able to derive an effective stochastic
process for the marginal statistics of a single component of the dynamics. This
allows us to design memory terms in the algorithm in such a way that the
resulting fields become Gaussian random variables allowing for an explicit
analysis. The asymptotic statistics of these fields are consistent with the
replica ansatz of the compressed sensing problem.Comment: 5 pages, accepted for ISIT 201
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.Comment: 31 pages, 10 figure
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