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In this paper, lossless and near-lossless compression algorithms for multichannel electroencephalogram (EEG) signals are presented based on image and volumetric coding. Multichannel EEG signals have significant correlation among spatially adjacent channels; moreover, EEG signals are also correlated across time. Suitable representations are proposed to utilize those correlations effectively. In particular, multichannel EEG is represented either in the form of image (matrix) or volumetric data (tensor), next a wavelet transform is applied to those EEG representations. The compression algorithms are designed following the principle of “lossy plus residual coding,” consisting of a wavelet-based lossy coding layer followed by arithmetic coding on the residual. Such approach guarantees a specifiable maximum error between original and reconstructed signals. The compression algorithms are applied to three different EEG datasets, each with different sampling rate and resolution. The proposed multichannel compression algorithms achieve attractive compression ratios compared to algorithms that compress individual channels separately.