Brain Source Localization in Head Harmonics Domain
Amita Giri, Lalan Kumar, Tapan Kumar Gandhi
Abstract
Brain source localization (BSL) using Electro- EncephaloGram (EEG) has been an active area of research because of its cost-effective and noninvasive nature of the operation. As the EEG data are spatially sampled over the head, the subsequent localization performance is limited by the head-shape assumption for efficient data representation. In the literature, the human head is approximated by spherical shape. Hence, spherical harmonics, the corresponding basis functions, have been the natural choice for EEG source reconstruction and localization. In this article, a new set of basis functions called Head Harmonics (H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) is developed to accurately represent the data sampled over head. The basis functions are formulated based on a more realistic head dimension. In addition, the forward model for source localization is presented in the H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> domain. Subsequently, H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> MUltiple SIgnal Classification (H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -MUSIC), H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> Recursive MUSIC (H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> R-MUSIC), and H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> Recursively Applied and Projected MUSIC (H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> RAP-MUSIC) methods are presented for BSL. For simulation, Root Mean Square Error (RMSE), computation time, and STandard Deviation (STD) ratio measures are utilized to evaluate the performance of the proposed algorithms. Real EEG data corresponding to visual stimulation, arithmetic task, and seizure are also utilized to validate the correctness of the proposed H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -based algorithms. The proposed model can be used with EEG instrumentation to localize neural sources for various real-time applications.