Chang Cai

Ali Hashemi, Yijing Gao, Chang Cai et al.

Several problems in neuroimaging and beyond require inference on the parameters of multi-task sparse hierarchical regression models. Examples include M/EEG inverse problems, neural encoding models for task-based fMRI analyses, and climate science. In these domains, both the model parameters to be inferred and the measurement noise may exhibit a complex spatio-temporal structure. Existing work either neglects the temporal structure or leads to computationally demanding inference schemes. Overcoming these limitations, we devise a novel flexible hierarchical Bayesian framework within which the spatio-temporal dynamics of model parameters and noise are modeled to have Kronecker product covariance structure. Inference in our framework is based on majorization-minimization optimization and has guaranteed convergence properties. Our highly efficient algorithms exploit the intrinsic Riemannian geometry of temporal autocovariance matrices. For stationary dynamics described by Toeplitz matrices, the theory of circulant embeddings is employed. We prove convex bounding properties and derive update rules of the resulting algorithms. On both synthetic and real neural data from M/EEG, we demonstrate that our methods lead to improved performance.

Gexin Huang, Jiawen Liang, Ke Liu et al.

Electromagnetic source imaging (ESI) requires solving a highly ill-posed inverse problem. To seek a unique solution, traditional ESI methods impose various forms of priors that may not accurately reflect the actual source properties, which may hinder their broad applications. To overcome this limitation, in this paper a novel data-synthesized spatio-temporally convolutional encoder-decoder network method termed DST-CedNet is proposed for ESI. DST-CedNet recasts ESI as a machine learning problem, where discriminative learning and latent-space representations are integrated in a convolutional encoder-decoder network (CedNet) to learn a robust mapping from the measured electroencephalography/magnetoencephalography (E/MEG) signals to the brain activity. In particular, by incorporating prior knowledge regarding dynamical brain activities, a novel data synthesis strategy is devised to generate large-scale samples for effectively training CedNet. This stands in contrast to traditional ESI methods where the prior information is often enforced via constraints primarily aimed for mathematical convenience. Extensive numerical experiments as well as analysis of a real MEG and Epilepsy EEG dataset demonstrate that DST-CedNet outperforms several state-of-the-art ESI methods in robustly estimating source signals under a variety of source configurations.