Phase Retrieval via Incremental Truncated Wirtinger Flow

TL;DR

This paper introduces an Incremental Truncated Wirtinger Flow algorithm for phase retrieval, demonstrating linear convergence and stability under noise, with optimal sample complexity and strong empirical performance.

Contribution

The paper proposes a novel incremental algorithm for phase retrieval that guarantees linear convergence and stability, improving upon existing methods.

Findings

Linear convergence to the true solution

Optimal sample complexity achieved

Effective performance on simulated and real data

Abstract

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.