GraHTP: A Provable Newton-like Algorithm for Sparse Phase Retrieval

TL;DR

This paper introduces GraHTP, a provable and efficient Newton-like algorithm for sparse phase retrieval that converges quadratically and outperforms existing methods in numerical experiments.

Contribution

The paper presents GraHTP, a novel non-convex algorithm with theoretical guarantees for sparse phase retrieval using complex sensing vectors.

Findings

Quadratic convergence rate of GraHTP after finite iterations

Superior performance of GraHTP over state-of-the-art algorithms

Low computational complexity per iteration

Abstract

This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit (GraHTP), for sparse phase retrieval with complex sensing vectors. GraHTP is theoretically provable and exhibits high efficiency, achieving a quadratic convergence rate after a finite number of iterations, while maintaining low computational complexity per iteration. Numerical experiments further demonstrate GraHTP's superior performance compared to state-of-the-art algorithms.