EEG Source Analysis [chapter]

Marco Congedo, Leslie Sherlin
<span title="">2011</span> <i title="Elsevier"> Neurofeedback and Neuromodulation Techniques and Applications </i> &nbsp;
doing so, notation has been simplified considerably and several symbols are used generically to represent objects of the same kind. Furthermore, I have employed both the Latin and Greek alphabet. The reader is invited to study carefully the section Notation and Nomenclature, after which the equations in the manuscript should result clear at first glance. If this is not the case then I have not succeeded in my endeavor. The chapter then collects basic known results in linear algebra and
more &raquo; ... s, to which the reader is referred throughout the ensuing chapters. All linear algebra results needed, with some more as a bonus, are collected in this section, named Linear Algebra. The expert reader may walk through quickly here. Finally, the chapter includes a short introduction to the physiology and physics of EEG, yielding the definition of the EEG sensor measurement, which is the starting point of all EEG data analysis, including the source analysis methods that we treat here. Chapter III introduces the family of regularized weighted minimum-norm inverse solutions. It addresses thus the problem of source localization. Emphasis is given to the two methods we have been using most, named sLORETA and eLORETA. Both the model driven and data driven version of these methods are presented, uncovering the connection with the well-known family of linearly constrained minimum-variance inverse solutions. Useful suggestions on the use of inverse solutions are provided. The chapter ends with a short overview of my contributions in regional current density estimations, particularly useful for real-time applications, including the use of data-independent filters known as beamformers and data-dependent filters designed to increase the signal to noise ratio, the classification accuracy, or any other sought purpose. This chapter has been included since inverse solutions are heavily employed in chapter VI and VII, hence I felt important to give an account of the mathematical background of these methods. Chapter IV, V, VI, VII teken together represent a long journey into the wide family of methods based on the diagonalization of matrices holding second-order statistics of the data (i.e., covariance matrices and similar). In Chapter IV a general framework for the (approximate) joint diagonalization of matrices estimated on multiple data sets is presented, showing that the same optimization in a leastsquared framework can be used to solve all problems encountered in these chapters. Two algorithms for solving the general optimization scheme are given. Chapter V treats basic spatial filters such as as principal component analysis, whitening, maximal covariance analysis, canonical correlation analysis and the common spatial pattern. The journey continue in Chapter VI with blind source separation (BSS) methods based on second-order statistics and associated algorithms, such as AMUSE, SOBI etc. In this chapter we investigate BSS theory and we provide a general conceptual framework and algorithm (AJDC) to deal with all major kinds of EEG data, namely, spontaneous, induced and evoked EEG. Finally, chapter VII treats group BSS methods and Joint BSS methods, which are extension of 7 the BSS methods when multiple subjects or multiple data sets are analyzed simultaneously. The different families of methods are illustrated with many real data examples. Chapter VIII and IX are the most original of the manuscript. Chapter VIII presents a new universal framework for BCI classification based on Riemann geometry. We show that the very same signal processing chain with minimal changes can be adapted to all current BCI modalities, including those based on the analysis of event-related (de)synchronizations, evoked-response potentials and steadystate evoked potentials. The framework is well adapted to support a new generation of multi-user BCI functioning without calibration. Our claim is supported with the classification of several data sets for each BCI modality. We believe firmly that the Riamannian framework will receive more and more attention in the BCI community and candidates to become the "standard" very much sought by the field. Chapter IX presents, rather exhaustively, current and very recent advances in differential Riemannian geometry and the affine-invariant metric, that is, it treats the theoretical bases allowing the results presented in chapter VIII. While the Riemannian framework is at first sight mathematically hostile, it turns out to be extremely simple in actual usage, much more simple that most advanced methods presented in chapter III-VII. The reader facing these tools for the first time is invited to tackle this chapter slowly, with an open-minded and challenging attitude. The chapter ends with some theoretical investigations we have started during the very last months, disclosing, among other things, some connections between the Riemannian distance and geometric mean with the material presented in chapter V, VI and VII. Riemann geometry has appeared in EEG literature only five years ago, but is gaining momentum very rapidly. The material presented in chapter VIII and IX is still completely or rather unknown to most EEG specialists. It has been included especially thinking to the members of the Jury, who I hope will find in this chapter new interesting and stimulating ideas, besides sharp results in the field of BCI. To conclude, Chapter X contains an overall discussion of the entire manuscript and some persectives for future research. Chapters III to IX form the core of the manuscript. They are self-contained, thus they may be read independently, although several cross-references are included to preserve the unity of the manuscript and to show connections between different research fields; after all, the methods presented in section III and those presented in chapters V-VII are clearly complementary, whereas the connections between the methods presented in chapter VIII-IX and those presented in the others are largely to be uncovered. Russian billionaire: eternal life" 2 . The goal of the so called "2045 Initiative" is to achieve, by 2045, the embedding of a brain with its consciousness in a chip. This is sometimes referred to as mind-tocomputer uploading. The billionaire at the origin of the project, which name is Dmitri Itskov, says: « I am going to get old and then die and all this for what? Life cannot resolve in this sad equation ». The project aims at an intermediary goal by 2020, which is to create an android avatar completely controlled by a BCI. Far from being just a rumor, it appears that the project has already involved several respectable and authoritative scientists. Again, BCI technology is evoked as a means to achieve what is naturally precluded to humans. Moreover, we must admit that the expectation is shared also by some experts. If yesterday I was perplexed, today I am puzzled. Why one may desire to "live" consciously in a chip? Wouldn't that be a nightmare? What could be human consciousness without human life? Undoubtedly, the possibility to allow communication without using the natural muscular and peripheral nerves pathways is a unique characteristic of BCI technology. This peculiarity fosters the dreams of the civilized mankind and there is nothing wrong in dreaming. However, we should be aware that BCI technology has risen in medical research -at least this has been its major showcase -as a possibility for those suffering of extremely disabling physical conditions preventing the communication with the external world. Today it is strongly motivated by military aims and is source of inspiration for the whole field of robotics. Put it simply, in my view pretending that BCI technology is meant to empower natural human abilities has nothing to do with science, thus I think it is about time for the BCI scientific community to start discussing seriously the many ethical questions concerning the role and purpose of BCI research in this world. 2
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