Doctoral Thesis Defense of Jair Montoya Martínez

Jair Montoya Martínez, a PhD student in the Signal Processing Group of the University Carlos III de Madrid will defend his doctoral thesis titled “Functional Brain Imaging on Mobile Devices by Solving the EEG Inverse Problem: a Structured Sparsity Approach” on December 5th

  • Title: “Functional Brain Imaging on Mobile Devices by Solving the EEG Inverse Problem: a Structured Sparsity Approach”
  • Advisor: Antonio Artés Rodríguez.
  • Event Date: Friday, December 5, 2014, 12:00 am.
  • Location: Adoración de Miguel (1.2.C16); Agustín de Betancourt Building; Leganés Campus; Universidad Carlos III de Madrid.

Abstract:

In this thesis we address the development of a mobile brain scanner, which is based on a wireless EEG neuroheadset, in charge of acquiring and transmitting the electrical potential measured on the scalp, and one mobile device (smartphone or tablet), in charge of receiving and processing these data to produce the cortical activation maps, which show, using a 3D brain model, the brain areas that are currently active. To generate the cortical activation maps, the mobile brain scanner needs to solve an electromagnetic inverse problem called the EEG inverse problem. The low spatial resolution of the EEG caused by the low conductivity of the skull plus the small number of EEG sensors available to capture the electrical activity produced by thousands of brain current sources, imply that the EEG inverse problem is underdetermined, ill-posed, and has infinite solutions. To make this problem tractable, in this thesis we assume that the number of active sources is small, that is, we assume that the set of active sources is a sparse set. Additionally, we also assume a linear relationship between the elements of this set. If we represent the set of brain current sources as a matrix (called the sources matrix), where the rows denote how the electrical activity of the sources vary over time, then the former assumptions lead to estimate a sources matrix which is structured sparse and low rank. To solve this problem, in this thesis we propose a method based on the factorization of the sources matrix as a product of two matrices: the first one encodes the spatial dynamics of the sources (how they change their spatial activation patterns), whereas the second one encodes their corresponding temporal dynamics (how they change their electrical activity over time). This method combines the ideas of the Group Lasso (structured sparsity) and Trace Norm (low rank) into one unified framework. We also develop and analyze the convergence of an alternating minimization algorithm to solve the resulting nonsmoothnonconvex regularization problem. Finally, in order to implement a working prototype of the mobile brain scanner, we bring our method to a real life scenario: online solving of the EEG inverse problem on a mobile device, which is continuously supplied with EEG data coming from the wireless EEG neuroheadset.