Quaternionic Reweighted Amplitude Flow for Phase Retrieval in Image Reconstruction

TL;DR

This paper introduces novel quaternionic algorithms for phase retrieval in image reconstruction, leveraging quaternion algebra to improve accuracy and efficiency in processing color signals.

Contribution

It develops the Quaternionic Reweighted Amplitude Flow (QRAF) and variants, along with the Quaternionic Perturbed Amplitude Flow (QPAF), advancing quaternionic phase retrieval methods.

Findings

Significantly improved recovery performance over existing methods.

Enhanced computational efficiency demonstrated on synthetic and real data.

QPAF achieves linear convergence in phase retrieval tasks.

Abstract

Quaternionic signal processing provides powerful tools for efficiently managing color signals by preserving the intrinsic correlations among signal dimensions through quaternion algebra. In this paper, we address the quaternionic phase retrieval problem by systematically developing novel algorithms based on an amplitude-based model. Specifically, we propose the Quaternionic Reweighted Amplitude Flow (QRAF) algorithm, which is further enhanced by three of its variants: incremental, accelerated, and adapted QRAF algorithms. In addition, we introduce the Quaternionic Perturbed Amplitude Flow (QPAF) algorithm, which has linear convergence. Extensive numerical experiments on both synthetic data and real images, demonstrate that our proposed methods significantly improve recovery performance and computational efficiency compared to state-of-the-art approaches.