The Physics and Mathematics of Electroencephalogram

This book focuses on a systematic introduction to the knowledge of mathematics and physics of electroencephalogram (EEG) and discusses an in-depth application of EEG and the development of new methods and technologies for mining and analyzing EEG. The Physics and Mathematics of Electroencephalogram offers a systematic overview of the technology for brain function and disease. It covers six parts: background knowledge of EEG, EEG forward problems, high-resolution EEG imaging, EEG inverse problems, EEG reference electrode, and EEG cloud platform. The author reviews the critical technologies in brain function and disease, such as EEG sourcing, EEG imaging, and EEG reference electrode standardization technique. The book's aim is to clarify the mechanism of EEG from the perspective of physics, mathematics, and engineering science to help multidisciplinary readers better understand and use EEG information more effectively. This book can be used as reference for researchers in the fields of neuroengineering, cognitive neuroscience, neurology, psychiatry, applied mathematics, and brain-like intelligence.

Dezhong Yao (Senior Member, IEEE) received the Ph.D. degree from the Chengdu University of Technology, Chengdu, China, in 1991. He is the Dean and founder, Sichuan Institute for Brain Science and Brain-Inspired Intelligence, University of Electronic Science and Technology of China (UESTC). His main research interests are Brain-X interaction including brain-computer interface, brainwave music interface, and Neuro-Imaging on music, epilepsy, cerebral palsy and plasticity.

1 Overview of EEG 2 Electromagnetics behind Brain Electric Field 3 Biophysics and Source Models of EEG 4 Brain Electrical Field in Regular Head Model 5 Brain Electric Field in Realistic Head Model 6 Theory of Equivalent Distributed Sources 7 High-Resolution Cortical Imaging 8 Scalp Laplacian Imaging 9 A Unified Framework for High-Resolution EEG 10 Basic Theory of EEG Inverse Problem 11 Signal Space-Based EEG Inverse Solution 12 Iterative Minimum Norm Solution 13 Zero-Reference for Scalp EEG 14 EEG Reference Selection