Demixing Structured Superposition Signals from Periodic and Aperiodic Nonlinear Observations

TL;DR

This paper introduces a new method for demixing multiple structured high-dimensional signals from limited nonlinear observations, achieving near-optimal sample complexity and outperforming previous techniques.

Contribution

The paper proposes a novel demixing algorithm that provably recovers components from nonlinear measurements with nearly optimal sample complexity, improving upon prior methods.

Findings

Method successfully recovers components with O(s) samples

Outperforms previous nonlinear demixing techniques

Validated through extensive simulations

Abstract

We consider the demixing problem of two (or more) structured high-dimensional vectors from a limited number of nonlinear observations where this nonlinearity is due to either a periodic or an aperiodic function. We study certain families of structured superposition models, and propose a method which provably recovers the components given (nearly) $m = \mathcal{O}(s)$ samples where $s$ denotes the sparsity level of the underlying components. This strictly improves upon previous nonlinear demixing techniques and asymptotically matches the best possible sample complexity. We also provide a range of simulations to illustrate the performance of the proposed algorithms.