2023/10/20 by Román Jácome, Jacome, Roman, Kumar Vijay Mishra +5
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Electron Microscopy Techniques and Applications #Advanced X-ray Imaging Techniques #Digital Holography and Microscopy #FOS: Computer and information sciences #FOS: Electrical engineering #Image and Video Processing (eess.IV) #Information Theory (cs.IT) #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2310.17660
openalex publication_date 2023/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing 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.