Beyond cosmic noon, galaxies usually appear as faint whispers amid overwhelming noise, yet this epoch is key to understanding massive galaxy assembly. ALMA’s sensitivity to cold dust and C II emission allows us to probe their interstellar media, but faint signals are still challenging, rendering robust de-noising essential. We aim to evaluate de-noising strategies---including classical statistical methods, sparse unsupervised representations, and supervised deep learning---to identify techniques that suppress noise while preserving flux and spectral--spatial morphology. We developed a physically motivated synthetic dataset of spectral cubes simulating rotating disc galaxies for training and evaluation. We benchmarked a principal component analysis (PCA), independent component analysis (ICA), iterative soft thresholding (IST) with 2D-1D wavelets, and a supervised 3D U-Net across peak S/Ns of ∼2. 5--8, applied to (i) toy cubes, (ii) synthetic C II IFU cubes from FIRE simulations, and (iii) ALMA observations of z galaxies from the CRISTAL sample and the quasar W2246-0526. Performance is assessed via root-mean-squared error (RMSE), flux conservation, morphology, and S/N improvement. The PCA and ICA provide limited noise reduction and struggle with correlated noise. IST reduces noise at moderate S/Ns, but can suppress emission at low S/Ns. The 3D U-Net outperforms IST on synthetic cubes, particularly at low S/N, though it may overestimate flux or hallucinate faint structures in this regime. On high S/N real data with relatively simple morphologies, the U-Net and IST achieve comparable performance. However, on low-S/N real data with complex morphologies not represented in the training set, the U-Net underperforms relative to IST, highlighting the challenges of generalisation beyond the training distribution. In ALMA-CRISTAL cubes, both IST and U-Net conserve >91% of flux and increase S/N by >6. For the extreme case of W2246--0526, the U-Net recovers sim80% of flux at moderate S/Ns, whereas IST robustly conserves flux and improves the S/N by sim3. Deep learning trained on synthetic data generalises effectively, though flux bias and interpretability challenges remain at low S/Ns. The addition of physically motivated priors and uncertainty quantification will enhance robustness. This framework of synthetic, simulated, and real datasets offers a pathway for transferable de-noising in surveys with ALMA, VLT/MUSE, and JWST IFUs.
Lahiry et al. (Sun,) studied this question.