Phase Retrieval via Incremental Truncated Wirtinger Flow
This addresses the phase retrieval problem for signal processing and imaging applications, with incremental improvements over existing methods.
The paper tackles the phase retrieval problem by proposing an algorithm called Incremental Truncated Wirtinger Flow, which converges linearly to the solution with optimal sample complexity and provides stability under noisy measurements.
In the phase retrieval problem, an unknown vector is to be recovered given quadratic measurements. This problem has received considerable attention in recent times. In this paper, we present an algorithm to solve a nonconvex formulation of the phase retrieval problem, that we call $\textit{Incremental Truncated Wirtinger Flow}$. Given random Gaussian sensing vectors, we prove that it converges linearly to the solution, with an optimal sample complexity. We also provide stability guarantees of the algorithm under noisy measurements. Performance and comparisons with existing algorithms are illustrated via numerical experiments on simulated and real data, with both random and structured sensing vectors.