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
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21 pages, 4 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:2310.17660
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.
Unfolding-Aided Bootstrapped Phase Retrieval in Optical Imaging
University of Manchester(曼彻斯特大学);Tampere University(坦佩雷大学);United States CCDC Army Research Laboratory(美国CCDC陆军研究实验室);University of Illinois Chicago(伊利诺伊大学芝加哥分校);Noiseless Imaging Ltd.(Noiseless成像有限公司)