Multidimensional Signal Processing

Multidimensional Signal Processing, Volume 54 in the Handbook of Statistics series is dedicated to presenting the latest developments and methodologies in multidimensional signal processing. The book aims to provide a comprehensive overview of the theories, models, and methods that form the foundation of this field. Chapters in this new release include Robust Parameter Estimation of Two Dimensional Chirp Model, Computability Theory for Multidimensional Signal Processing, Tensor signal processing, Spectral compressed sensing by structured matrix optimization methods, Space-time imaging, Hypercomplex Widely Linear Processing, and much more. The book's chapters are meticulously curated to offer detailed, educational content rather than conventional journal-style articles. Other chapters cover Hypercomplex phase retrieval, Hypercomplex widely linear estimation, MIMO radar signal processing, Computational lidar, Signal processing applications of higher-dimensional graphs, Space-Time Radio Signal Processing by Photonic Upconversion, Computational imaging, and Topology identification and learning over graphs using multi-dimensional data.

Table of Contents:
Preface 1. Robust Parameter Estimation of Two Dimensional Chirp Model Debassis Kundu 2. Computability Theory for Multidimensional Signal Processing Holger Boche, Volker Pohl and H. VIncent Poor 3. Tensor signal processing David Hong 4. Spectral compressed sensing by structured matrix optimization methods Jian-Feng Cai, Xunmeng Wu, Zai Yang and Juntao You 5. Space-time imaging David Brady 6. Hypercomplex Widely Linear Processing Sayed Pouria Talebi and Clive Cheong Took 7. Hypercomplex phase retrieval Kumar Vijay Mishra, Henry Arguello and Brian M. Sadler 8. Hypercomplex widely linear estimation Wenyuan Wang and Kutluyil Dogancay 9. MIMO radar signal processing Sergiy A. Vorobyov and Visa Koivunen 10. Computational lidar Gonzalo R. Arce 11. Signal processing applications of higher-dimensional graphs Santiago Segarra 12. Space-Time Radio Signal Processing by Photonic Upconversion Xiao-Feng Qi and Dennis W. Prather 13. Computational imaging Ayush Bhandari 14. Topology identification and learning over graphs using multi-dimensional data Gonzalo Mateos, Georgios Giannakis, Yanning Shen and Ananthram Swami

About the Author :
Arni S.R. Srinivasa Rao works in pure mathematics, applied mathematics, probability, artificial intelligence and applications in medicine. He developed the concept of “Exact Deep Learning Machines”, which can provide designs for accurate predictions without any uncertainty. He had edited these handbooks jointly with renowned statistician Dr. C. R. Rao. He is a Professor at the Medical College of Georgia, Augusta University, U.S.A., and the Director of the Laboratory for Theory and Mathematical Modeling housed within the Division of Infectious Diseases, Medical College of Georgia, Augusta, U.S.A. Previously, Dr. Rao conducted research and/or taught at the Mathematical Institute, University of Oxford (2003, 2005-07), Indian Statistical Institute (1998-2002, 2006-2012), Indian Institute of Science (2002-04), University of Guelph (2004-06). Until 2012, Dr. Rao held a permanent faculty position at the Indian Statistical Institute. He has won the Heiwa-Nakajima Award (Japan) and Fast Track Young Scientists Fellowship in Mathematical Sciences (DST, New Delhi). Dr. Rao also proved a major theorem in stationary population models, such as, Rao’s Partition Theorem inPopulations, Rao-Carey Theorem in stationary populations, and developed mathematical modeling-based policies for the spread of diseases like HIV, H5N1, COVID-19, etc. He developed a new set of network models for understanding avian pathogen biology on grid graphs (these were called chicken walk models), AI Models for COVID-19, and received wide coverage in the science media. Dr. Rao is an elected Fellow of ISMMACS (Indian Society for Mathematical Modeling and Computer Simulation), and ISPS (Indian Society for Probability and Statistics). He developed concepts such as “Multilevel Contours within a bundle of Complex Number Planes”. Kumar Vijay Mishra obtained a Ph.D. in electrical engineering and M.S. in mathematics from The University of Iowa in 2015, and M.S. in electrical engineering from Colorado State University in 2012, while working on NASA’s Global Precipitation Mission Ground Validation (GPM-GV) weather radars. He received his B. Tech. summa cum laude (Gold Medal, Honors) in electronics and communication engineering from the National Institute of Technology, Hamirpur (NITH), India in 2003. He is a Senior Fellow at the United States DEVCOM Army Research Laboratory and Technical Adviser to Singapore-based automotive radar start-up Hertzwell. He has served as the Distinguished Lecturer (DL) of IEEE Communications Society (2023-2024), IEEE Aerospace and Electronic Systems Society (AESS) (2023-2024, 2025-2026), IEEE Vehicular Technology Society (2023-2025, 2025-2027), and IEEE Geoscience and Remote Sensing Society (2024-2025). He is the recipient of the IEEE Signal Processing Society Pierre-Simon Laplace Early Career Technical Achievement Award (2024), IET Premium Best Paper Prize (2021), U. S. National Academies Harry Diamond Distinguished Fellowship (2018-2021), Viterbi Postdoctoral Fellowship (2015, 2016), Lady Davis Postdoctoral Fellowship (2017), DRDO LRDE Scientist of the Year Award (2006), and NITH Director’s Gold Medal (2003). He is Chair (2023-2026) of the International Union of Radio Science (URSI) Commission C, Chair (2025-) of IEEE AESS Technical Working Group on Integrated Sensing and Communications (ISAC-TWG), and Vice-Chair (2021-present) of the IEEE Synthetic Aperture Standards Committee. He is Editor-in-Chief of River Rapids Series in Radar Systems, Signal Processing, Antennas and Electromagnetics (2025-). He has been Senior Area Editor of IEEE Transactions on Signal Processing (2024-), Associate Editor of IEEE Transactions on Aerospace and Electronic Systems (2020-) and IEEE Transactions on Antennas and Propagation (2023-). He has edited five books on signal processing and radar. His research interests include radar systems, signal processing, remote sensing, and electromagnetics Gonzalo R. Arce is the Charles Black Evans Professor of Electrical and Computer Engineering at the University of Delaware and a JPMorgan Chase Senior Faculty Fellow. He obtained a Ph.D. in electrical engineering from Purdue University. A leading voice in multidimensional signal processing, his work spans nonlinear signal processing, compressive sensing, graph‑based signal processing, and computational imaging—with notable advances in computational lidar from space, spectral and tomographic imaging with coded‑aperture systems, computational lithography, and green noise halftoning. He leads the Computational Imaging and Machine Learning Laboratory at the University of Delaware. He is a Fellow of the IEEE, OPTICA (formerly OSA), SPIE, and the National Academy of Inventors, and a two‑time Fulbright–Nokia Distinguished Chair in Communications and Information Technologies at Aalto University in Helsinki, Finland. He currently serves as Editor‑in‑Chief of the IEEE Transactions on Computational Imaging. He is the author or editor of several foundational texts, including Nonlinear Signal Processing (Wiley), Nonlinear Signal and Image Processing (CRC), Computational Lithography (Wiley), Modern Digital Halftoning (CRC Press), and his research bridges rigorous mathematics with deployable imaging systems used from spectral X‑ray tomography to compressive LiDAR.