Localization of Brain Signals by Alternating Projection.

A popular approach for modeling brain activity in MEG and EEG is based on a small set of current dipoles, where each dipole represents the combined activation of a local area of the brain. Here, we address the problem of multiple dipole localization with a novel solution called Alternating Projection (AP). The AP solution is based on minimizing the least-squares (LS) criterion by transforming the multi-dimensional optimization required for direct LS solution, to a sequential and iterative solution in which one source at a time is localized, while keeping the other sources fixed. Results from simulated, phantom, and human MEG data demonstrated the high accuracy of the AP method, with superior localization results than popular scanning methods from the multiple-signal classification (MUSIC) and beamformer families. In addition, the AP method was more robust to forward model errors resulting from head rotations and translations, as well as different cortex tessellation grids for the forward and inverse solutions, with consistently higher localization accuracy in low SNR and highly correlated sources.

LOCALIZATION OF SPATIALLY EXTENDED BRAIN SOURCES BY FLEXIBLE ALTERNATING PROJECTION (FLEX-AP).

Magnetoencephalography (MEG) and electroencephalography (EEG) are widely employed techniques for the in-vivo measurement of neural activity with exceptional temporal resolution. Modeling the neural sources underlying these signals is of high interest for both neuroscience research and pathology. The method of Alternating Projection (AP) was recently shown to outperform the well-established recursively applied and projected multiple signal classification (RAP-MUSIC) algorithm. In this work, we further enhanced AP to allow for source extent estimation, a novel approach termed flexible extent AP (FLEX-AP). We found that FLEX-AP achieves significantly lower errors for spatially coherent sources compared to AP, RAP-MUSIC, and the corresponding extension, FLEX-RAP-MUSIC. We also found an advantage for discrete dipoles under forward modeling errors encountered in real-world scenarios. Together, our results indicate that the FLEX-AP method can unify dipole fitting and distributed source imaging into a single algorithm with promising accuracy.

An F-ratio-based method for estimating the number of active sources in MEG.

Introduction: Magnetoencephalography (MEG) is a powerful technique for studying the human brain function. However, accurately estimating the number of sources that contribute to the MEG recordings remains a challenging problem due to the low signal-to-noise ratio (SNR), the presence of correlated sources, inaccuracies in head modeling, and variations in individual anatomy. Methods: To address these issues, our study introduces a robust method for accurately estimating the number of active sources in the brain based on the F-ratio statistical approach, which allows for a comparison between a full model with a higher number of sources and a reduced model with fewer sources. Using this approach, we developed a formal statistical procedure that sequentially increases the number of sources in the multiple dipole localization problem until all sources are found. Results: Our results revealed that the selection of thresholds plays a critical role in determining the method's overall performance, and appropriate thresholds needed to be adjusted for the number of sources and SNR levels, while they remained largely invariant to different inter-source correlations, translational modeling inaccuracies, and different cortical anatomies. By identifying optimal thresholds and validating our F-ratio-based method in simulated, real phantom, and human MEG data, we demonstrated the superiority of our F-ratio-based method over existing state-of-the-art statistical approaches, such as the Akaike Information Criterion (AIC) and Minimum Description Length (MDL). Discussion: Overall, when tuned for optimal selection of thresholds, our method offers researchers a precise tool to estimate the true number of active brain sources and accurately model brain function.

Encoder-Decoder Architecture for 3D Seismic Inversion.

Inverting seismic data to build 3D geological structures is a challenging task due to the overwhelming amount of acquired seismic data, and the very-high computational load due to iterative numerical solutions of the wave equation, as required by industry-standard tools such as Full Waveform Inversion (FWI). For example, in an area with surface dimensions of 4.5 km × 4.5 km, hundreds of seismic shot-gather cubes are required for 3D model reconstruction, leading to Terabytes of recorded data. This paper presents a deep learning solution for the reconstruction of realistic 3D models in the presence of field noise recorded in seismic surveys. We implement and analyze a convolutional encoder-decoder architecture that efficiently processes the entire collection of hundreds of seismic shot-gather cubes. The proposed solution demonstrates that realistic 3D models can be reconstructed with a structural similarity index measure (SSIM) of 0.9143 (out of 1.0) in the presence of field noise at 10 dB signal-to-noise ratio.

MEG Source Localization via Deep Learning.

We present a deep learning solution to the problem of localization of magnetoencephalography (MEG) brain signals. The proposed deep model architectures are tuned to single and multiple time point MEG data, and can estimate varying numbers of dipole sources. Results from simulated MEG data on the cortical surface of a real human subject demonstrated improvements against the popular RAP-MUSIC localization algorithm in specific scenarios with varying SNR levels, inter-source correlation values, and number of sources. Importantly, the deep learning models had robust performance to forward model errors resulting from head translation and rotation and a significant reduction in computation time, to a fraction of 1 ms, paving the way to real-time MEG source localization.

Linear-time subspace clustering via bipartite graph modeling.

We present a linear-time subspace clustering approach that combines sparse representations and bipartite graph modeling. The signals are modeled as drawn from a union of low-dimensional subspaces, and each signal is represented by a sparse combination of basis elements, termed atoms, which form the columns of a dictionary matrix. The sparse representation coefficients are arranged in a sparse affinity matrix, which defines a bipartite graph of two disjoint sets: 1) atoms and 2) signals. Subspace clustering is obtained by applying low-complexity spectral bipartite graph clustering that exploits the small number of atoms for complexity reduction. The complexity of the proposed approach is linear in the number of signals, thus it can rapidly cluster very large data collections. Performance evaluation of face clustering and temporal video segmentation demonstrates comparable clustering accuracies to state-of-the-art at a significantly lower computational load.