$L^0$-regularized Variational Methods for Sparse Phase Retrieval

TL;DR

This paper introduces L0-regularized variational methods for sparse phase retrieval, employing ADMM algorithms with convergence guarantees to efficiently recover sparse signals from phaseless measurements, outperforming existing methods.

Contribution

The paper develops novel L0-regularized variational models for sparse phase retrieval and proposes efficient ADMM algorithms with closed-form solutions and convergence guarantees.

Findings

Higher successful recovery rates compared to state-of-the-art methods.

Lower computational cost in each iteration.

Effective recovery from noisy measurements.

Abstract

We study the problem of recovering the underlining sparse signals from clean or noisy phaseless measurements. Due to the sparse prior of signals, we adopt an L0regularized variational model to ensure only a small number of nonzero elements being recovered in the signal and two different formulations are established in the modeling based on the choices of data fidelity, i.e., L2and L1norms. We also propose efficient algorithms based on the Alternating Direction Method of Multipliers (ADMM) with convergence guarantee and nearly optimal computational complexity. Thanks to the existence of closed-form solutions to all subproblems, the proposed algorithm is very efficient with low computational cost in each iteration. Numerous experiments show that our proposed methods can recover sparse signals from phaseless measurements with higher successful recovery rates and lower computation cost compared with the state-of-art methods.