Simultaneous EEG-fMRI is a multi-modal neuroimaging technique that provides complementary spatial and temporal resolution for inferring a latent source space of neural activity. In this paper we address this inference problem within the framework of transcoding -- mapping from a specific encoding (modality) to a decoding (the latent source space) and then encoding the latent source space to the other modality. Specifically, we develop a symmetric method consisting of a cyclic convolutional transcoder that transcodes EEG to fMRI and vice versa. Without any prior knowledge of either the hemodynamic response function or lead field matrix, the method exploits the temporal and spatial relationships between the modalities and latent source spaces to learn these mappings. We show, for real EEG-fMRI data, how well the modalities can be transcoded from one to another as well as the source spaces that are recovered, all on unseen data. In addition to enabling a new way to symmetrically infer a latent source space, the method can also be seen as low-cost computational neuroimaging -- i.e. generating an expensive fMRI BOLD image from low cost EEG data.
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