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arXiv 2602.23946eess.SPcs.ITeess.IVmath.IT
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超复数相位恢复

Hypercomplex Phase Retrieval

United States DEVCOM Army Research Laboratory(美国DEVCOM陆军研究实验室);Universidad Industrial de Santander(桑坦德工业大学);The University of Texas, Austin(德克萨斯大学奥斯汀分校)

Kumar Vijay Mishra, Henry Arguello, Brian M. Sadler

AI总结:

本文探讨了超复数相位恢复问题,通过超复数方法在光学成像中实现信号恢复,提出新的算法和理论框架。

摘要:

超复数信号处理(HSP)通过显式利用各维度之间的相关性,利用克莱因代数对多维信号进行分析和处理,提供了强大的工具。近年来,超复数形式的相位恢复(PR)问题,即从仅强度测量中恢复复值信号,引起了越来越多的兴趣。超复数相位恢复(HPR)自然出现在光学成像和计算传感应用中,其中信号通常使用四元数或八元数值表示。与经典PR类似,HPR问题可能涉及通过复数、超复数、傅里叶或其他结构化传感算子获得的测量。这些形式为开发先进的HSP基于算法和理论框架开辟了新途径。本章回顾了HPR新兴的方法和应用,特别强调光学成像系统。

英文摘要:

Hypercomplex signal processing (HSP) offers powerful tools for analyzing and processing multidimensional signals by explicitly exploiting inter-dimensional correlations through Clifford algebra. In recent years, hypercomplex formulations of the phase retrieval (PR) problem, wheren a complex-valued signal is recovered from intensity-only measurements, have attracted growing interest. Hypercomplex phase retrieval (HPR) naturally arises in a range of optical imaging and computational sensing applications, where signals are often modeled using quaternion- or octonion-valued representations. Similar to classical PR, HPR problems may involve measurements obtained via complex, hypercomplex, Fourier, or other structured sensing operators. These formulations open new avenues for the development of advanced HSP-based algorithms and theoretical frameworks. This chapter surveys emerging methodologies and applications of HPR, with particular emphasis on optical imaging systems.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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