Demixing sparse signals from nonlinear observations

Mohammadreza Soltani, Chinmay Hegde

Abstract: Signal demixing is of special importance in several applications ranging from astronomy to computer vision. The goal in demixing is to recover a set of signals from their linear superposition. In this paper, we study the more challenging scenario where only a limited number of nonlinear measurements of the signal superposition are available. Our contribution is a simple, fast algorithm that recovers the component signals from the nonlinear measurements. We support our algorithm with a rigorous theoretical analysis, and provide upper bounds on the estimation error as well as the sample complexity of demixing the components (up to a scalar ambiguity). We also provide a range of simulation results, and observe that the method outperforms a previous algorithm based on convex relaxation.