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

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.