基于随机多分辨率扫描的近场和远场EEG源定位（RAMUS）中的连续指数先验
Conditionally Exponential Prior in Focal Near- and Far-Field EEG Source Localization via Randomized Multiresolution Scanning (RAMUS)
摘要：
在本文中，我们专注于非侵入性脑电重建与皮层和弱可检测的深层成分的分布脑活动的逆问题。特别是，我们的目标是推广以前广泛使用的条件高斯先验（CGP）形式主义，以实现更高的焦点分布重建。为此，我们引入了一个分层先验，一般的指数分布，简称为条件指数先验（CEP）。一级CEP对应于执行拉普拉斯先验的聚焦性，其遭受强烈的深度偏差，使得深部活动不可恢复。我们通过RAMUS在多个分辨率级别上进行采样，以减少这种偏差，因为众所周知，这取决于源空间的分辨率。此外，我们引入了一个程序的基础上的生理先验知识的大脑活动，以获得形状和尺度参数的伽玛超先验，引导CEP。后验估计使用迭代统计方法，期望最大化和迭代交替顺序算法，我们证明是算法相似，并具有密切的相似性，迭代重新加权方法计算。CEP的性能进行了比较，最近的采样为基础的偶极子定位方法序贯半解析蒙特卡罗估计（SEARCH）在模拟体感诱发电位相关的人正中神经刺激的数值实验。我们的研究结果表明，一级CEP和RAMUS的混合可以实现与二级病例（CGP）相当的准确性，同时更聚焦。此外，所提出的混合被证明是强大的噪声影响，并比较以及与SEESTRUCTURE获得的偶极子重建。
英文摘要：
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. 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, refered to as conditionally exponential prior (CEP). The first-degree CEP corresponds to focality enforcing Laplace prior that suffers from strong depth bias 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 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 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 compare well to the dipole reconstructions obtained with SESAME.
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