用四元数重加权法提升彩色图像相位恢复精度与速度
Quaternionic Reweighted Amplitude Flow for Phase Retrieval in Image Reconstruction
- 基于幅度模型设计四元数重加权算法，保留多通道相关性
- 在真实图像上实现比现有方法更高的恢复精度和更快收敛
- 适合处理彩色图像重建的科研人员与工程应用者
四元数信号处理通过四元数代数有效保持信号维度间的内在关联，为高效处理彩色信号提供强大工具。本文系统地针对四元数相位恢复问题，提出基于幅度模型的新算法。具体而言，提出四元数重加权幅度流（QRAF）算法，并进一步设计了增量式、加速式和自适应式三种变体。此外，引入具有线性收敛性的四元数扰动幅度流（QPAF）算法。在合成数据与真实图像上的大量数值实验表明，所提方法在恢复性能和计算效率方面显著优于当前最优方法。
原文摘要 · Abstract (English)
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.
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