This book offers a unified introduction to low-rank Hankel methods for modern spectral signal processing, which are widely used in high-resolution radar/sonar imaging, DOA estimation and array processing, massive MIMO channel estimation, medical and astronomical imaging, and integrated sensing and communication systems. It provides a practical pathway from basic Hankel structures to state-of-the-art algorithms for spectral compressed sensing, blind super-resolution, and joint blind super-resolution and demixing. Focusing on spectrally sparse signals, the book shows how to exploit Hankel matrix and tensor structures to recover continuous-domain frequencies from few, noisy, or nonuniform samples. It explains when convex approaches based on nuclear or atomic norms guarantee exact recovery, and why they become computationally prohibitive in large-scale radar, imaging, and communication systems. Building on this foundation, the text introduces fast nonconvex schemes—projected, vanilla, scaled, and Riemannian gradient methods—that leverage low-rank factorization of Hankel (and vectorized Hankel) matrices with rigorous convergence and sample complexity guarantees. A central theme is handling realistic, “blind” scenarios where point spread functions or channels are unknown, and multi-user mixtures must be demixed before super-resolving fine spectral details. The book systematically treats these challenges, from single-measurement spectral compressed sensing to multi-measurement Hankel tensor completion and integrated sensing-and-communication style joint blind super-resolution and demixing. Throughout, theoretical insights are closely linked to algorithm design and numerical behavior, helping readers understand not only how to implement methods, but when and why they work. This volume targets advanced graduate students, researchers, and R&D engineers in signal processing, applied mathematics, radar and wireless communications, and related areas who need reliable and efficient tools for spectral compressed sensing, blind super-resolution, and demixing in high-dimensional applications.

Dr. Xu Zhang is an Assistant Professor of Artificial Intelligence at Xidian University and formerly a Postdoctoral Fellow at the Chinese Academy of Sciences. His research focuses on signal processing, optimization, and machine learning, with key contributions to blind super-resolution and spectral compressed sensing in leading venues.

Dr. Jinchi Chen is an Associate Professor of Mathematics at East China University of Science and Technology. His work lies at the interface of signal processing, numerical optimization, and data science, with extensive publications on blind super-resolution, spectrally sparse signal recovery, compressed sensing, and low-rank matrix and tensor methods.

Dr. Jinsheng Li is a Researcher at the Future Technology Research Center of China Telecom Research Institute. His research interests include non-convex optimization for signal processing, low-rank matrix recovery, and DOA estimation, with several IEEE Transactions on Signal Processing papers on fast algorithms for blind super-resolution and spectral compressed sensing.