When 12-lead electrocardiograms (ECGs) are printed on paper, the original 10-second recording is conventionally cut into 2.5-second segments so that all leads fit on a single page, resulting in discarding most of the recorded signal. We investigate whether it is feasible to recover the full 10-second, 12-lead signal after digitizing scanned paper ECGs using a 1D convolutional U-Net with self-attention in the bottleneck, trained on the PTB-XL database. The reconstructed signals achieved a root mean squared error (RMSE) of 0.11 and a Pearson correlation coefficient (PCC) of 0.87 across all leads when compared with the original signal on a held-out test set of 4368 recordings. Reconstructed and original signals were delineated using NeuroKit2, and the resulting R-, P-, Q-, S- and T-peak amplitudes and RR-, QT- and PR-intervals were compared using RMSE, R^2-score and PCC. R- and T-peaks and the RR-interval were reconstructed most reliably (Pearson (r) = 0.61, 0.82 and 0.91, respectively), while the S-peak was reconstructed poorly (r = 0.13). From qualitative assessment, we saw that reconstructed signals were systematically smoother and lower in amplitude than the originals. The proposed approach appears somewhat feasible, but it may still lack the robustness needed to reliably reconstruct data for downstream applications intended for clinical deployment.