A fast iterative algorithm for demixing sparse signals from nonlinear observations

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.