  Simulations of complex-valued Hopfield networks based on spin-torque
oscillators can recover phase-encoded images. Sequences of memristor-augmented
inverters provide tunable delay elements that implement complex weights by
phase shifting the oscillatory output of the oscillators. Pseudo-inverse
training suffices to store at least 12 images in a set of 192 oscillators,
representing 16$\times$12 pixel images. The energy required to recover an image
depends on the desired error level. For the oscillators and circuitry
considered here, 5 % root mean square deviations from the ideal image require
approximately 5 $\mu$s and consume roughly 130 nJ. Simulations show that the
network functions well when the resonant frequency of the oscillators can be
tuned to have a fractional spread less than $10^{-3}$, depending on the
strength of the feedback.
