  Recent progress in the application of color centers to nanoscale spin sensing
makes the combined use of noise spectroscopy and scanning probe imaging an
attractive route for the characterization of arbitrary material systems.
Unfortunately, the traditional approach to characterizing the environmental
magnetic field fluctuations from the measured probe signal typically requires
the experimenter's input, thus complicating the implementation of automated
imaging protocols based on spectrally resolved noise. Here, we probe the
response of color centers in diamond in the presence of externally engineered
random magnetic signals, and implement a deep neural network to methodically
extract information on their associated spectral densities. Building on a long
sequence of successive measurements under different types of stimuli, we show
that our network manages to efficiently reconstruct the spectral density of the
underlying fluctuating magnetic field with good fidelity under a broad set of
conditions and with only a minimal measured data set, even in the presence of
substantial experimental noise. These proof-of-principle results create
opportunities for the application of machine-learning methods to
color-center-based nanoscale sensing and imaging.
