Demixing Structured Superposition Signals from Periodic and Aperiodic Nonlinear Observations
This work addresses a demixing problem in signal processing with potential applications in data analysis, offering a significant improvement over prior nonlinear techniques.
The paper tackles the problem of demixing structured high-dimensional vectors from nonlinear observations, achieving recovery with nearly optimal sample complexity of m = O(s) samples, where s is the sparsity level, which asymptotically matches the best possible performance.
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.