Local multilayer analytic sensing for EEG source localization: Performance bounds and experimental results

Abstract

Analytic sensing is a new mathematical framework to estimate the parameters of a multi-dipole source model from boundary measurements. The method deploys two working principles. First, the sensing principle relates the boundary measurements to the volumetric interactions of the sources with the so-called "analytic sensor," a test function that is concentrated around a singular point outside the domain of interest. Second, the annihilation principle allows retrieving the projection of the dipoles' positions in a single shot by polynomial root finding. Here, we propose to apply analytic sensing in a local way; i.e., the poles are not surrounding the complete domain. By combining two local projections of the (nearby) dipolar sources, we are able to reconstruct the full 3-D information. We demonstrate the feasibility of the proposed approach for both synthetic and experimental data, together with the theoretical lower bounds of the localization error.

3D reconstruction of wave-propagated point sources from boundary measurements using joint sparsity and finite rate of innovation

“…Several mathematical models can apply, such as Poisson's equation for electroencephalography (EEG) [1], the heat equation for diffusive source localization [2], or the wave equation for acoustic sources [3]. Here, we focus on boundary measurements for systems goverend by the wave equation.…”

Finite rate of innovation with non-uniform samples

“…Examples of such signals include streams of Diracs, piecewise polynomials and piecewise sinusoidals. Very efficient SVD-based algorithms exist when the sampling kernels are periodized sinc kernels [3], modulated Gaussians [4], Strang-Fix kernels [5,6] and even Cauchy-like analytic kernels [7].…”