We propose a novel functional data framework for artifact extraction and removal to estimate brain electrical activity sources from EEG signals. Our methodology is derived on the basis of event related potential (ERP) analysis, and motivated by mapping adverse artifactual events caused by body movements and physiological activity originated outside the brain. A functional independent component analysis (FICA) based on the use of fourth moments is conducted on the principal component expansion in terms of B-spline basis functions. We extend this model setup by introducing a discrete roughness penalty in the orthonormality constraint of the functional principal component decomposition to later compute estimates of FICA. Compared to other ICA algorithms, our method combines a regularization mechanism stemmed from the principal eigendirections with a discrete penalization given by the $d$-order difference operator. In this regard, it allows to naturally control high-frequency remnants of neural origin overlapping latent artifactual eigenfunctions and thus to preserve this persistent activity at artifact extraction level. Furthermore, we introduce a new cross-validation method for the selection of the penalization parameter which uses shrinkage to asses the performance of the estimators for functional representations with larger basis dimension and excess of roughness. This method is used in combination with a kurtosis measure in order to provide the optimal number of independent components.The FICA model is illustrated at functional and longitudinal dimensions by an example on real EEG data where a subject willingly performs arm gestures and stereotyped physiological artifacts. Our method can be relevant in neurocognitive research and related fields, particularlly in situations where movement can bias the estimation of brain potentials.
翻译:我们提出一个新的人工制品提取和清除功能数据框架,以估计来自EEG信号的脑电动源。我们的方法是根据与事件相关的潜在(ERP)分析得出的,其动机是绘制由大脑外的身体运动和生理活动引起的有害原生事件图,根据使用四分钟进行功能独立的部件分析(ICSA),根据B-spline基函数对主要组成部分扩展进行功能性独立分析(FICA)。我们扩大这一模型的设置,在功能主要组成部分的正态性约束中引入一种离散的粗糙处罚,将其扩展至后来的FICA估算。与ICA的其他算法相比,我们的方法将源自主要天体运动和源于大脑运动的由大脑运动和由美元-顺序差异操作者提供的离散的惩罚性惩罚机制结合起来。在这方面,可以自然控制高频率的神经源残留,重叠的潜伏性耐动机能,从而保持这种耐久性的活动。此外,我们采用新的交叉验证方法选择惩罚性参数,该参数使用缩缩压来评估粗糙的大脑变化状况,在功能性分析中采用一种功能性结构结构结构的过度分析方法,在功能性分析中进行更精确的演算,在最佳的模型中可以进行更深的模型中进行一个说明。