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Coarse-grained models have provided researchers with greatly improved computational efficiency in modeling structures and dynamics of biomacromolecules, but, to be practically useful, they need fast and accurate conversion methods back to the all-atom representation. Reconstruction of atomic details may also be required in the case of some experimental methods, like electron microscopy, which may provide Cα-only structures. In this contribution, we present a new method for recovery of all backbone atom positions from just the Cα coordinates. Our approach, called deepBBQ, uses a deep convolutional neural network to predict a single internal coordinate per peptide plate, based on Cα trace geometric features, and then proceeds to recalculate the cartesian coordinates based on the assumption that the peptide plate atoms lie in the same plane. Extensive comparison with similar programs shows that our solution is accurate and cost-efficient. The deepBBQ program is available as part of the open-source bioinformatics toolkit Bioshell and is free for download and the documentation is available online.