Single-Frame Super-Resolution of Solar Magnetograms: Investigating Physics-Based Metrics & Losses

TL;DR

The paper addresses cross-instrument inconsistencies in solar magnetograms and demonstrates a physics-informed single-frame super-resolution approach to upsample MDI data to HMI resolution and cross-calibrate instrument characteristics. It uses HighRes-net for SR with a gradient-based loss to preserve magnetic-field physics, showing that including Sobel-gradient penalties improves both pixel distributions and multi-scale entropy relative to baselines. The results indicate substantial improvements over bicubic upsampling or MSE alone, particularly in preserving large-field regions and sharp structures. This approach enables construction of a uniform, long-term high-resolution magnetogram dataset across decades, facilitating more reliable space weather studies.

Abstract

Breakthroughs in our understanding of physical phenomena have traditionally followed improvements in instrumentation. Studies of the magnetic field of the Sun, and its influence on the solar dynamo and space weather events, have benefited from improvements in resolution and measurement frequency of new instruments. However, in order to fully understand the solar cycle, high-quality data across time-scales longer than the typical lifespan of a solar instrument are required. At the moment, discrepancies between measurement surveys prevent the combined use of all available data. In this work, we show that machine learning can help bridge the gap between measurement surveys by learning to super-resolve low-resolution magnetic field images and translate between characteristics of contemporary instruments in orbit. We also introduce the notion of physics-based metrics and losses for super-resolution to preserve underlying physics and constrain the solution space of possible super-resolution outputs.

Figures (6)

• Figure 1: Comparison of co-temporal, co-aligned magnetograms obtained by MDI ( left), and HMI ( right). Both images show the full solar disk, re-scaled as if they were observed from $1$ Astronomical Unit, and plotted over the range of $\pm2000$ Gauss. The $128^{\prime\prime} \times 128^{\prime\prime}$ insets were registered using vertical and horizontal shifts to account for the distortion between instruments.
• Figure 2: Difference between the a) mean and b) standard deviation of the pixel values of the HR HMI target and SR output as a function of training epochs.
• Figure 3: Correlation plots of pixel values of the HR HMI target and SR output, using a) an MSE loss and b) an MSE + gradient-based loss function.
• Figure 4: Comparison of magnetogram patches using different loss functions. Left to right: a) LR MDI input, b) bicubic upsampling, c) MSE loss, d) MSE + gradient-based loss, e) HR HMI target.
• Figure 5: a) Pixel histograms and b) multi-scale entropy of the HR HMI target, bicubic upsampling, and the SR output using an MSE, or MSE + gradient-based loss function.