This paper develops a novel statistical approach to characterize temporally localised cross-oscillatory interactions between channels in a functional brain network. Brain signals are generally nonstationary and the proposed framework uses wavelets as an effective tool for capturing (i) single-scale channel transient features, due to their adaptiveness to the dynamic signal properties, and (ii) cross-scale channel interactions, due to their multi-scale nature. Our approach formalises scale-specific subprocesses and cross-scale (CS) dependencies for a new class of multivariate locally stationary (MvLSW) wavelet processes that we refer to as CS-MvLSW. Under this model, we develop a novel spectral domain time-varying cross-scale dependence measure and its appropriate estimation. Extensive simulation studies demonstrate that the theoretically established properties hold in practice. The proposed CS-MvLSW framework remains accurate under pronounced cross-scale dependence, whereas existing MvLSW modelling can deteriorate even for single-scale coherence when such complex structure is present in the process. The proposed cross-scale analysis is applied to electroencephalogram (EEG) data to study alterations in the functional connectivity structure in children diagnosed with attention deficit hyperactivity disorder (ADHD). Our approach identified novel, clinically pertinent cross-scale interactions in the functional brain network, differentiating brain connectivity between control and ADHD groups.

翻译：本文提出了一种新颖的统计方法，用于刻画功能性脑网络中通道间具有时间局部性的交叉振荡相互作用。脑信号通常是非平稳的，所提出的框架利用小波作为有效工具来捕捉：(i) 由于小波对动态信号特性的自适应性，能够捕获单尺度通道的瞬态特征；(ii) 由于其多尺度特性，能够捕获跨尺度通道的相互作用。我们的方法形式化地描述了新一类多元局部平稳小波过程（我们称之为CS-MvLSW）中尺度特定的子过程以及跨尺度依赖关系。在此模型下，我们提出了一种新颖的谱域时变跨尺度依赖度量及其相应的估计方法。大量的模拟研究表明，理论建立的性质在实践中成立。所提出的CS-MvLSW框架在显著的跨尺度依赖下仍保持准确性，而现有的MvLSW建模方法即使对于单尺度相干性，当过程中存在此类复杂结构时，其性能也可能下降。所提出的跨尺度分析方法应用于脑电图数据，以研究被诊断为注意力缺陷多动障碍儿童的功能性连接结构的变化。我们的方法识别了功能性脑网络中新颖且具有临床意义的跨尺度相互作用，从而区分了对照组与ADHD组之间的脑连接差异。