In this paper, we propose an iterative algorithm based on hard thresholding
for demixing a pair of signals from nonlinear observations of
their superposition. We focus on the under-determined case where
the number of available observations is far less than the ambient dimension
of the signals. We derive nearly-tight upper bounds on the
sample complexity of the algorithm to achieve stable recovery of the
component signals. Moreover, we show that the algorithm enjoys
a linear convergence rate. We provide a range of simulations to illustrate
the performance of the algorithm both on synthetic and real
data.