David Korda¹, Jan Jurčák¹, Michal Švanda^1,2, and Nazaret Bello González³

1 Astronomical Institute of the Czech Academy of Sciences, Fričova 298, 25165 Ondřejov, Czech Republic
2 Astronomical Institute, Charles University, V Holešovičkách 2, 18000 Prague, Czech Republic
3 Institut für Sonnenphysik (KIS), Georges-Köhler-Allee 401A, 79110 Freiburg im Breisgau, Germany

SDO/HMI provides full-disk observations of the Sun with high cadence and continuous coverage but with a limited spatial resolution. In contrast, Hinode/SOT-SP delivers spectro-polarimetric data at much higher resolution, though over a smaller field of view and with lower temporal cadence. Bridging these two instruments would enable studies of dynamic solar magnetic structures with high spatial detail across the full disk and over long timescales.

We developed a deep-learning-based method to enhance the spatial resolution of HMI observations—both continuum intensity and the full vector magnetic field—toward Hinode/SOT-SP quality. Our model uses a convolutional neural network trained on synthetic HMI-like inputs, derived by degrading Hinode data to match HMI resolution and noise. This avoids the need for co-aligned HMI–Hinode observations, which suffer from imperfect alignment at granular scales—the very scales to which convolutional networks are most sensitive.

Earlier studies such as Ref [1] demonstrated the feasibility of neural enhancement using synthetic HMI training data, focusing on intensity and line-of-sight magnetic fields. More recently, Wang et al.^[2] used co-aligned HMI and Hinode/SOT-SP data for training. However, the spatial mismatch between these instruments’ limits accuracy when training at small scales. In our approach, the use of degraded Hinode data as input ensures perfect alignment and more reliable ground truth for training. For technical details and evaluation metrics, see Ref [3].

To simulate realistic HMI-like data, we applied the exact HMI point-spread function to Hinode/SOT-SP maps and injected synthetic noise drawn from the same statistical distribution as HMI noise. This step proved essential—especially for correctly reconstructing horizontal magnetic fields, which are dominated by disambiguation noise. The model was trained on small patches of continuum intensity, field strength, and the three magnetic field components in the local solar frame. Rare but important structures such as strong sunspot cores and horizontal penumbral fields were emphasized through a custom loss function.

Figure 1. Comparison between standard HMI, HMI-like (degraded Hinode), and original SOT-SP observations is shown for both continuum intensity and the zonal magnetic field. The degraded Hinode data closely match the HMI observations, both visually and statistically, including noise characteristics. Although the co-alignment is not exact, it clearly illustrates that HMI-like data closely match HMI in resolution and noise.

Once trained, the model shows excellent agreement with Hinode/SOT-SP data across all quantities. Figure 2 displays pixel-to-pixel comparisons for intensity and magnetic field. The plots use a logarithmic colour scale to highlight that large-error points are rare. Most points fall tightly along the one-to-one line, especially at high magnetic field amplitudes where the model performs with very low error. At low field strengths, the model effectively suppresses disambiguation noise. As a result, it produces clean output in these regions—but when compared to Hinode data, which retains its own noise and disambiguation artefacts, this leads to increased scatter, as visible in the figure. This highlights the fact that the model denoises both horizontal and vertical field components, recovering meaningful structure even in noise-dominated regions.

Figure 2. Log-density pixel-to-pixel correspondence for intensity and magnetic field. The vast majority of values lie near the diagonal.

To evaluate the model under real conditions, we applied it to full-disk HMI observations of active region AR 12203 on 3 November 2014. The model successfully recovered HMI fine structure in both continuum intensity and vector magnetic field, including penumbral filaments and compact magnetic concentrations that are difficult to resolve in native HMI data. Importantly, the model generalizes well to new data without introducing artifacts or overfitting.

Figure 3. Example of application to real HMI observations of AR 12203. The model restores fine structure in both continuum and vector field components, even in noisy data.

This neural deconvolution method outperforms both traditional algorithms (e.g. Richardson–Lucy) and previous neural models that lacked proper noise handling or ignored horizontal magnetic fields. It provides a practical way to generate high-resolution, full-disk, high-cadence magnetic field and intensity maps. The enhanced data are suitable for a wide range of applications in studies of active region dynamics and evolution.

All code and pretrained models are freely available: GitHub: Sirrah91/HMI_to_SP

References

[1] Díaz Baso, C. J., & Asensio Ramos, A. 2018, A&A, 614, A5 (Also, HMI Science Nugget #103)
[2] Wang, R., Fouhey, D. F., Higgins, R. E. L., et al. 2024, ApJ, 970, 168
[3] Korda, D., et al. 2025, A&A, 697, A28