Deep and sparse de-noising benchmarks for spectral data cubes of high-z galaxies: From simulations to ALMA observations

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.