  Nuclear magnetic resonance imaging (MRI) at the atomic scale offers exciting
prospects for determining the structure and function of individual molecules
and proteins. Quantum defects in diamond have recently emerged as a promising
platform towards reaching this goal, and allowed for the detection and
localization of single nuclear spins under ambient conditions. We present an
efficient strategy for extending imaging to large nuclear spin clusters,
fulfilling an important requirement towards a single-molecule MRI technique.
Our method combines the concepts of weak quantum measurements, phase encoding
and simulated annealing to detect three-dimensional positions from many nuclei
in parallel. Detection is spatially selective, allowing us to probe nuclei at a
chosen target radius while avoiding interference from strongly-coupled proximal
nuclei. We demonstrate our strategy by imaging clusters containing more than 20
carbon-13 nuclear spins within a radius of 2.4 nm from single, near-surface
nitrogen--vacancy centers at room temperature. The radius extrapolates to 7-8
nm for protons. Beside taking an important step in nanoscale MRI, our
experiment also provides an efficient tool for the characterization of large
nuclear spin registers in the context of quantum simulators and quantum network
nodes.
