# Quaternionic Reweighted Amplitude Flow for Phase Retrieval in Image Reconstruction

arXiv: https://arxiv.org/abs/2501.02180 · HTML: https://mlsanity.com/paper/2501.02180/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 4 Jan 2025.

## Builds on (most cited first, 9 of 9)

- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [A Geometric Analysis of Phase Retrieval](https://mlsanity.com/paper/1602.06664/) (2016)
- [Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow](https://mlsanity.com/paper/1605.08285/) (2016)
- [Color image recovery using low-rank quaternion matrix completion algorithm](https://mlsanity.com/paper/1909.06567/) (2019)
- [Quaternion Nuclear Norm minus Frobenius Norm Minimization for color image reconstruction](https://mlsanity.com/paper/2409.07797/) (2024)
- [A New Cross-Space Total Variation Regularization Model for Color Image Restoration with Quaternion Blur Operator](https://mlsanity.com/paper/2405.12114/) (2024)
- [Phase Retrieval of Quaternion Signal via Wirtinger Flow](https://mlsanity.com/paper/2210.14170/) (2022)
- [Convex Quaternion Optimization for Signal Processing: Theory and Applications](https://mlsanity.com/paper/2305.06879/) (2023)
- [Octonion Phase Retrieval](https://mlsanity.com/paper/2308.15784/) (2023)

## Abstract (arXiv)

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.