This paper develops mathematical methods for localizing focal sources at different depths based on the non-invasive electro-/magnetoencephalography measurements. In the context of hierarchical Bayesian modelling, we introduce a conditionally exponential prior (CEP) which extends the concept of the conditionally Gaussian prior (CGP) and has been proposed to be advantageous in reconstructing far-field activity, in particular, when coupled with randomized multiresolution scanning (RAMUS). An approach to obtain the shape and scale parameter of the gamma hyperprior steering the CEP is derived from the physiological a priori knowledge of the brain activity. The core concept of this study is to show that the first-degree CEP will yield and improve the focality compared to the second-order case. The results of the present numerical experiments suggest that sources reconstructed via a combination of the first-degree CEP and RAMUS achieve an accuracy comparable to the second-degree case while being more focal for numerically simulated originators of human somatosensory evoked potentials (SEPs) related to human median nerve stimulation, including simultaneous thalamic and cortical activity, as well as for a sub-thalamic dipolar and quadrupolar source configuration.

翻译：本文根据非侵入性电/磁脉动测量测量结果,为不同深度的焦点源定位开发了数学方法。在Bayesian等级建模方面,我们采用了一个有条件的指数前(CEP)方法,扩展了有条件高斯先前(CGP)的概念,并提议该方法有利于重建远方活动,特别是在与随机多分辨率扫描(RAUS)相结合的情况下,尤其有利于重建远方活动。一种获取伽马超光谱导的形状和比例参数的方法来自CEP对大脑活动的生理先验知识。本研究的核心概念是表明,一级CEPEP将产生并改进与二级案例相比的焦点。目前的数字实验结果表明,通过一级CEP和RAUS相结合而重建的来源的精确度可与二度情况相近。同时,CEP是人类中中神经刺激(包括同步的极地表和共振动的二次振动源)相关人类超振动潜力(SEPOPs)的模拟发端点。