Conditionally Exponential Prior in Focal Near- and Far-Field EEG Source Localization via Randomized Multiresolution Scanning (RAMUS)

Abstract

In this paper, we focus on the inverse problem of reconstructing distributional brain activity with cortical and weakly detectable deep components in non-invasive Electroencephalography. We consider a recently introduced hybrid reconstruction strategy combining a hierarchical Bayesian model to incorporate a priori information and the advanced randomized multiresolution scanning (RAMUS) source space decomposition approach to reduce modelling errors, respectively. In particular, we aim to generalize the previously extensively used conditionally Gaussian prior (CGP) formalism to achieve distributional reconstructions with higher focality. For this purpose, we introduce as a hierarchical prior, a general exponential distribution, which we refer to as conditionally exponential prior (CEP). The first-degree CEP corresponds to focality enforcing Laplace prior, but it also suffers from strong depth bias, when applied in numerical modelling, making the deep activity unrecoverable. We sample over multiple resolution levels via RAMUS to reduce this bias as it is known to depend on the resolution of the source space. Moreover, we introduce a procedure based on the physiological a priori knowledge of the brain activity to obtain the shape and scale parameters of the gamma hyperprior that steer the CEP. The posterior estimates are calculated using iterative statistical methods, expectation maximization and iterative alternating sequential algorithm, which we show to be algorithmically similar and to have a close resemblance to the iterative ell _1 and ell _2 reweighting methods. The performance of CEP is compared with the recent sampling-based dipole localization method Sequential semi-analytic Monte Carlo estimation (SESAME) in numerical experiments of simulated somatosensory evoked potentials related to the human median nerve stimulation. Our results obtained using synthetic sources suggest that a hybrid of the first-degree CEP and RAMUS can achieve an accuracy comparable to the second-degree case (CGP) while being more focal. Further, the proposed hybrid is shown to be robust to noise effects and compares well with the dipole reconstructions obtained with SESAME.