A Graph Fourier Transform Based Bidirectional Long Short-Term Memory Neural Network for Electrophysiological Source Imaging

Abstract

Electrophysiological source imaging (ESI) refers to the process of reconstructing underlying activated sources on the cortex given the brain signal measured by Electroencephalography (EEG) or Magnetoencephalography (MEG). Due to the ill-posed nature of ESI, solving ESI requires the design of neurophysiologically plausible regularization or priors to guarantee a unique solution. Recovering focally extended sources is more challenging, and traditionally uses a total variation regularization to promote spatial continuity of the activated sources. In this paper, we propose to use graph Fourier transform (GFT) based bidirectional long-short term memory (BiLSTM) neural network to solve the ESI problem. The GFT delineates the 3D source space into spatially high, medium and low frequency subspaces spanned by corresponding eigenvectors. The low frequency components can naturally serve as a spatially low-band pass filter to reconstruct extended areas of source activation. The BiLSTM is adopted to learn the mapping relationship between the projection of low-frequency graph space and the recorded EEG. Numerical results show the proposed GFT-BiLSTM outperforms other benchmark algorithms in synthetic data under varied signal-to-noise ratios (SNRs). Real data experiments also demonstrate its capability of localizing the epileptogenic zone of epilepsy patients with good accuracy.

Evaluation of Long-Short Term Memory Networks for M/EEG Source Imaging with Simulated and Real EEG Data

“…However, since ANN-based inverse solutions only work with a given electrode/sensor layout, anatomy and source space, pre-trained models could only be used for generic cases (i.e., template brains and electrode layouts) or would require retraining with the individual electrode layout and source space by replacing the input and output layers. Another option would be to compress the output space as described by Jiao et al (2022), leading to fewer neurons in the output layer.…”

“…The ANN-based inverse solutions for distributed dipole models all suffer from the high computational complexity given by the large number of dipoles (typically ≈ 10 3 to 10 4 vertices) that directly determine the size of the output layer, leading to large numbers of parameters. Jiao et al (2022) proposed a Graph Fourier Transform of the vertices’ adjacency matrix to reduce the number of dipoles. This works by selecting only a subset of the eigenvectors required to represent sparse source configurations, which in their case led to a reduction from 2,052 to 615 output nodes, thereby minimizing the number of parameters and thus computation time of their proposed bidirectional LSTM architecture.…”

Personalized Deep Learning based Source Imaging Framework Improves the Imaging of Epileptic Sources from MEG Interictal Spikes

“…Deep learning methods have the advantage of implicitly learning the source distributions instead of explicitly formulating the regularization terms, providing opportunities for a more accurate and robust ESI estimate. There have been several attempts recently to image brain activities using deep neural networks [55][56][57][58][59][60]. They have shown excellent performance in computer simulations, demonstrating the power of DL-based ESI methods.…”

Extended Brain Sources Estimation via Unrolled Optimization Neural Network

“…In order to encourage source extents estimation, Ding proposed to use a sparse constraint in the transformed domain by introducing TV defined from the irregular 3D mesh [22]. Other researchers used the same TV definition such as [4,[23][24][25]. The TV was defined to be the 1 norm of the first order spatial gradient using a linear transform matrix V ∈ R P ×N with its definition can be found in [22], where N is the number of voxels/sources, P equals the sum of the degrees of all source nodes.…”