  The reconstruction of electrical current densities from magnetic field
measurements is an important technique with applications in materials science,
circuit design, quality control, plasma physics, and biology. Analytic
reconstruction methods exist for planar currents, but break down in the
presence of high spatial frequency noise or large standoff distance,
restricting the types of systems that can be studied. Here, we demonstrate the
use of a deep convolutional neural network for current density reconstruction
from two-dimensional (2D) images of vector magnetic fields acquired by a
quantum diamond microscope (QDM) utilizing a surface layer of Nitrogen Vacancy
(NV) centers in diamond. Trained network performance significantly exceeds
analytic reconstruction for data with high noise or large standoff distances.
This machine learning technique can perform quality inversions on lower SNR
data, reducing the data collection time by a factor of about 400 and permitting
reconstructions of weaker and three-dimensional current sources.
