  Individual electron spins have been observed using magnetic resonance in
combination with a number of distinct detection approaches. The coordinates of
an individual electron spin can then in principle be determined by introducing
a 10 to 100 nm diameter magnetic needle, scanning the needle, and collecting
signal as a function of the needle's position. Although individual electrons
have recently been localized with nanometer precision in this way using a
nitrogen-vacancy center in diamond as the spin detector, the experiment's low
signal-to-noise ratio limited acquisition to two-dimensional scanning of just a
few dozen data points and was incompatible with nitroxide spin labels widely
used to label proteins and nucleic acids. We introduce and numerically simulate
a protocol for detecting and imaging individual nitroxide electron spins
mechanically with high spatial resolution. In our protocol a scanned
magnet-tipped cantilever is brought near the sample, modulated microwaves are
applied to resonantly excite electron spins, and changes in spin magnetization
are detected as a shift in the mechanical frequency of the cantilever. By
carefully applying resonant microwaves in short bursts in synchrony with the
cantilever's oscillation, we propose to retain high spatial resolution even at
large cantilever amplitude where sensitivity is highest. Numerical simulations
reveal nanometer-diameter rings of frequency-shift signal as the tip is
scanned. Our primary finding is that it is possible --- using a Bayesian,
reverse Monte Carlo algorithm introduced here --- to obtain the full
three-dimensional distribution of electron coordinates from the signal rings
revealed in a two-dimensional frequency-shift map. This reduction in
dimensionality brings within reach, on a practical timescale, the
angstrom-resolution three-dimensional imaging of spin-labeled macromolecules.
