Improving the Temporal Resolution of SOHO/MDI Magnetograms of Solar Active Regions Using a Deep Generative Model

TL;DR

This work introduces GenMDI, a conditional diffusion framework for temporal super-resolution of SOHO/MDI LOS magnetograms, enabling synthetic frames to be inserted between observed magnetograms by conditioning on neighboring frames to preserve dynamical evolution in solar active regions. Trained on triplets of MDI magnetograms, GenMDI uses a diffusion process on the difference between true frames and linearly interpolated frames, guided by a two-input U-Net+ architecture with self-attention, and demonstrates superior performance over linear interpolation in PCC, PSNR, and CMF metrics. The method enables extending temporal cadence from 96 minutes to as fine as 12 minutes and validates against HMI observations in overlapping periods, suggesting GenMDI can produce temporally consistent, higher-resolution magnetogram sequences that facilitate studies of magnetic field evolution. The approach lays groundwork for creating a uniform, long-baseline SOHO–SDO data set, potentially bridging observational gaps and enhancing space weather investigations, with future work exploring diffusion-GAN hybrids and vector magnetogram generation.

Abstract

We present a novel deep generative model, named GenMDI, to improve the temporal resolution of line-of-sight (LOS) magnetograms of solar active regions (ARs) collected by the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO). Unlike previous studies that focus primarily on spatial super-resolution of MDI magnetograms, our approach can perform temporal super-resolution, which generates and inserts synthetic data between observed MDI magnetograms, thus providing finer temporal structure and enhanced details in the LOS data. The GenMDI model employs a conditional diffusion process, which synthesizes images by considering both preceding and subsequent magnetograms, ensuring that the generated images are not only of high-quality, but also temporally coherent with the surrounding data. Experimental results show that the GenMDI model performs better than the traditional linear interpolation method, especially in ARs with dynamic evolution in magnetic fields.

Figures (7)

• Figure 1: Illustration of the forward and reverse diffusion processes. (a) For a triplet of images $(\mathbf{w}, \mathbf{x}, \mathbf{y})$, we calculate the difference images $(\mathbf{x} - \mathbf{x}_{I})$ and $(\mathbf{y}-\mathbf{w})$, where $\mathbf{x}_{I}$ is obtained by applying linear interpolation to $\mathbf{w}$ and $\mathbf{y}$. (b) In the forward diffusion process, we gradually add noise to the original difference image $\mathbf{x}_0$ = $(\mathbf{x} - \mathbf{x}_{I})$ to transform it to the Gaussian noise $\mathbf{\mathbf{x}}_T$. (c) In the reverse diffusion process, we start from $\mathbf{x}_T$ along with the conditional image $(\mathbf{y}-\mathbf{w})$ and attempt to denoise $\mathbf{x}_T$ into the original difference image $\mathbf{x}_0$.
• Figure 2: The inference process of GenMDI. The trained U-Net$^{+}$ model in GenMDI takes as input $\hat{\mathbf{x}}_T$, which is a randomly generated Gaussian noise image, along with the conditional image $(\mathbf{y} - \mathbf{w})$, and predicts as output a synthetic difference image $\hat{\mathbf{x}}_0$, which approximates the original difference image $\mathbf{x}_0$ = $(\mathbf{x} - \mathbf{x}_{I})$ in Figure \ref{['fig:normaldiff']}. The conditional image $(\mathbf{y} - \mathbf{w})$ is used to guide the model inference process. Note that red lines represent the data flow of the input/output images. Blue lines represent the control flow of the iterative procedure used by the GenMDI model.
• Figure 3: Performance comparison between our GenMDI model and the linear interpolation (LI) method on the whole test set. GemMDI performs better than LI in all metrics.
• Figure 4: Comparison between the magnetograms produced by the GenMDI model and the LI method on AR 9240. (Top panels) Three consecutive observed MDI magnetograms, enclosed by black boundary lines, are taken at 22:24 UT on 30 November 2000, and at 00:00 UT and 01:36 UT on 1 December 2000 respectively, with a cadence of 96 minutes. The synthetic magnetogram at 00:00 UT on 1 December 2000, enclosed by a red (blue, respectively) boundary line, is interpolated by the LI method (predicted by the GenMDI model, respectively). (Bottom panels) The FOV of the region highlighted by the yellow box in each corresponding magnetogram in the top row is displayed. The areas pointed to by the red and blue arrows show differences between the LI-interpolated magnetogram and GenMDI-predicted magnetogram. The areas pointed to by the yellow arrows highlight differences among the observed magnetograms at different times.
• Figure 5: Comparison between the magnetograms produced by the GenMDI model and the LI method on AR 9802. (Top panels) Three consecutive observed MDI magnetograms, enclosed by black boundary lines, are taken at 17:36 UT, 19:12 UT and 20:48 UT respectively on 4 February 2002, with a cadence of 96 minutes. The synthetic magnetogram at 19:12 UT on 4 February 2002, enclosed by a red (blue, respectively) boundary line, is interpolated by the LI method (predicted by the GenMDI model, respectively). (Bottom panels) The FOV of the region highlighted by the yellow box in each corresponding magnetogram in the top row is displayed. The areas pointed to by the red and blue arrows show differences between the LI-interpolated magnetogram and GenMDI-predicted magnetogram. The areas pointed to by the yellow arrows highlight differences among the observed magnetograms at different times.