Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing the intrinsic correlation of the signal dimensions through Clifford algebra. Recently, the hypercomplex representation of the phase retrieval (PR) problem, wherein a complex-valued signal is estimated through its intensity-only projections, has attracted significant interest. The hypercomplex PR (HPR) arises in many optical imaging and computational sensing applications that usually comprise quaternion- and octonion-valued signals. Analogous to the traditional PR, measurements in HPR may involve complex, hypercomplex, Fourier, and other sensing matrices. This set of problems opens opportunities for developing novel HSP tools and algorithms. This article provides a synopsis of the emerging areas and applications of HPR with a focus on optical imaging.

中文翻译：

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超复杂相位检索邀请：理论与应用[超复杂信号和图像处理]


超复杂信号处理 (HSP) 提供了最先进的工具，通过克利福德代数利用信号维度的内在相关性来处理多维信号。最近，相位检索（PR）问题的超复杂表示（其中通过仅强度投影来估计复值信号）引起了人们的极大兴趣。超复数 PR (HPR) 出现在许多光学成像和计算传感应用中，这些应用通常包含四元数和八元数值信号。与传统的 PR 类似，HPR 中的测量可能涉及复杂、超复杂、傅立叶和其他传感矩阵。这组问题为开发新颖的 HSP 工具和算法提供了机会。本文概述了 HPR 的新兴领域和应用，重点关注光学成像。