用超复数方法解决光学成像中的相位恢复问题。
Hypercomplex Phase Retrieval
- 基于克利福德代数的超复数信号处理，建模多维信号关联。
- 在四元数、八元数表示下实现强度测量中的相位恢复。
- 适合光学成像与计算传感领域的研究人员参考。
超复数信号处理（HSP）通过克利福德代数显式利用多维信号间的跨维度相关性，为分析和处理多维信号提供强大工具。近年来，将相位恢复（PR）问题以超复数形式表述——即从仅含强度的测量中恢复复值信号——引起了广泛关注。超复数相位恢复（HPR）自然出现在多种光学成像和计算传感应用中，这些场景常采用四元数或八元数表示信号。与经典相位恢复类似，HPR问题可涉及通过复数、超复数、傅里叶或其他结构化传感算子获取的测量。这些公式为基于HSP的先进算法和理论框架的发展开辟了新途径。本章综述了HPR的新兴方法与应用，尤其聚焦于光学成像系统。
原文摘要 · Abstract (English)
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.
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