Bayesian Spatial Blind Source Separation via the Thresholded Gaussian Process

Blind source separation (BSS) aims to separate latent source signals from their mixtures. For spatially dependent signals in high-dimensional and large-scale data, such as neuroimaging, most existing BSS methods do not take into account the spatial dependence and the sparsity of the latent source signals. To address these major limitations, we propose a Bayesian spatial blind source separation (BSP-BSS) approach for neuroimaging data analysis. We assume the expectation of the observed images as a linear mixture of multiple sparse and piece-wise smooth latent source signals, for which we construct a new class of Bayesian nonparametric prior models by thresholding Gaussian processes. We assign the vMF priors to mixing coefficients in the model. Under some regularity conditions, we show that the proposed method has several desirable theoretical properties including the large support for the priors, the consistency of joint posterior distribution of the latent source intensity functions and the mixing coefficients, and the selection consistency on the number of latent sources. We use extensive simulation studies and an analysis of the resting-state fMRI data in the Autism Brain Imaging Data Exchange (ABIDE) study to demonstrate that BSP-BSS outperforms the existing method for separating latent brain networks and detecting activated brain activation in the latent sources. Supplementary materials for this article are available online.

盲源分离（Blind Source Separation，BSS）旨在从混合信号中分离出潜在源信号。针对神经影像学等大规模高维数据中的空间依赖信号，现有多数BSS方法未考虑潜在源信号的空间依赖性与稀疏性。为解决这些核心局限，我们提出一种面向神经影像学数据分析的贝叶斯空间盲源分离（Bayesian Spatial Blind Source Separation，BSP-BSS）方法。我们假设观测影像的期望为多个稀疏且分段平滑的潜在源信号的线性混合，并通过阈值化高斯过程构建了一类全新的贝叶斯非参数先验模型。我们为模型中的混合系数赋予vMF先验分布。在若干正则性条件下，我们证明所提方法具备多项优良理论性质：包括先验的宽支撑性、潜在源强度函数与混合系数的联合后验分布一致性，以及潜在源数量的选择一致性。我们通过大量仿真实验与自闭症脑成像数据交换（Autism Brain Imaging Data Exchange，ABIDE）研究中的静息态功能磁共振成像（resting-state fMRI）数据分析，证实BSP-BSS在分离潜在脑网络、检测潜在源中的激活脑区方面均优于现有方法。本文补充材料可在线获取。