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We present a simple, but novel, hybrid approach to hyperspectral data cube reconstruction from computed tomography imaging spectrometry (CTIS) images that sequentially combines neural networks and the iterative expectation maximisation (EM) algorithm. We train and test the ability of the method to reconstruct data cubes of 100 × 100 × 25 and 100 × 100 × 100 voxels, corresponding to 25 and 100 spectral channels, from simulated CTIS images generated by our CTIS simulator. The hybrid approach utilises the inherent strength of the Convolutional Neural Network (CNN) with regards to noise and its ability to yield consistent reconstructions and make use of the EM algorithm’s ability to generalise to spectral images of any object without training. The hybrid approach achieves better performance than both the CNNs and EM alone for seen (included in CNN training) and unseen (excluded from CNN training) cubes for both the 25- and 100-channel cases. For the 25 spectral channels, the improvements from CNN to the hybrid model (CNN + EM) in terms of the mean-squared errors are between 14 % and 26 %. For 100 spectral channels, the improvements between 19 % and 40 % are attained with the largest improvement of 40 % for the unseen data, to which the CNNs are not exposed during the training.

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