Estimating intracranial current sources underlying the electromagnetic signals observed from extracranial sensors is a perennial challenge in non-invasive neuroimaging. Established solutions to this inverse problem treat time samples independently without considering the temporal dynamics of event-related brain processes. This paper describes current source estimation from simultaneously recorded magneto- and electro-encephalography (MEEG) using a recurrent neural network (RNN) that learns sequential relationships from neural data. The RNN was trained in two phases: (1) pre-training and (2) transfer learning with L1 regularization applied to the source estimation layer. Performance of using scaled labels derived from MEEG, magnetoencephalography (MEG), or electroencephalography (EEG) were compared, as were results from volumetric source space with free dipole orientation and surface source space with fixed dipole orientation. Exact low-resolution electromagnetic tomography (eLORETA) and mixed-norm L1/L2 (MxNE) source estimation methods were also applied to these data for comparison with the RNN method. The RNN approach outperformed other methods in terms of output signal-to-noise ratio, correlation and mean-squared error metrics evaluated against reference event-related field (ERF) and event-related potential (ERP) waveforms. Using MEEG labels with fixed-orientation surface sources produced the most consistent estimates. To estimate sources of ERF and ERP waveforms, the RNN generates temporal dynamics within its internal computational units, driven by sequential structure in neural data used as training labels. It thus provides a data-driven model of computational transformations from psychophysiological events into corresponding event-related neural signals, which is unique among MEEG source reconstruction solutions.

Analysis of neuroimaging data (e.g., Magnetic Resonance Imaging, structural and functional MRI) plays an important role in monitoring brain dynamics and probing brain structures. Neuroimaging data are multi-featured and non-linear by nature, and it is a natural way to organise these data as tensors prior to performing automated analyses such as discrimination of neurological disorders like Parkinson's Disease (PD) and Attention Deficit and Hyperactivity Disorder (ADHD). However, the existing approaches are often subject to performance bottlenecks (e.g., conventional feature extraction and deep learning based feature construction), as these can lose the structural information that correlates multiple data dimensions or/and demands excessive empirical and application-specific settings. This study proposes a Deep Factor Learning model on a Hilbert Basis tensor (namely, HB-DFL) to automatically derive latent low-dimensional and concise factors of tensors. This is achieved through the application of multiple Convolutional Neural Networks (CNNs) in a non-linear manner along all possible dimensions with no assumed a priori knowledge. HB-DFL leverages the Hilbert basis tensor to enhance the stability of the solution by regularizing the core tensor to allow any component in a certain domain to interact with any component in the other dimensions. The final multi-domain features are handled through another multi-branch CNN to achieve reliable classification, exemplified here using MRI discrimination as a typical case. A case study of MRI discrimination has been performed on public MRI datasets for discrimination of PD and ADHD. Results indicate that 1) HB-DFL outperforms the counterparts in terms of FIT, mSIR and stability (mSC and umSC) of factor learning; 2) HB-DFL identifies PD and ADHD with an accuracy significantly higher than state-of-the-art methods do. Overall, HB-DFL has significant potentials for neuroimaging data analysis applications with its stability of automatic construction of structural features.