Enhancing Solar Continuum Resolution Using SDO/HMI-ONSET Data

1.   INTRODUCTION

The multi-wavelength high-resolution solar observational framework constitutes a cornerstone paradigm in contemporary solar physics, deriving its scientific significance from global collaborative diagnostics of multi-scale and multi-physical processes in the solar atmosphere. Advanced multi-scale imaging techniques spanning ultraviolet to radio wavelengths have progressively revealed couplings between the photospheric magnetic fields, chromospheric heating, and coronal mass ejections. Continuum observations, serving as a cornerstone for radiative energy transport diagnostics, atmospheric stratification, and space weather modeling, play an irreplaceable role in deciphering solar magnetic field dynamics and energy release mechanisms. Early studies using ground-based telescopes (e.g., the Multi-Layer Spectrograph at Big Bear Solar Observatory) with single-band observations revealed correlations between the photospheric granulation convection and magnetic field distributions.^[1] Concurrently, space-based platforms such as SOHO/MDI achieved the first long-term stable monitoring of full-disk magnetic fields, providing critical data support for the evolution of the solar cycle.^[2] With technological advancements, multi-wavelength synoptic observations have emerged as the mainstream paradigm. For example, the Ganyu Station of the Purple Mountain Observatory (Chinese Academy of Sciences) employed high-temporal-resolution (20–30 frames per second) Hα and white-light joint observations to identify the contraction–expansion dynamics of flare loops during their initial phases, uncovering multi-scale characteristics of magnetic reconnection.^[3] At the application level, time-series analyses linking continuum-derived photospheric magnetic field evolution to multi-band eruptive signatures (e.g., extreme ultraviolet waves and hard X-ray sources) have significantly enhanced the causal predictability of space weather events. This progress has catalyzed a paradigm shift from empirical warning paradigms (e.g., sunspot group classification) to physics-driven predictive frameworks.

The Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO)^[4], operational since 2010, has accumulated high-quality continuum data spanning complete solar cycles, leveraging its 45-s cadence and full-disk imaging capability (4096 × 4096 pixels)^[5]. HMI’s standardized data-processing pipeline (flat-field correction residuals of <0.5% per year) ensures temporal consistency, making it ideal for machine-learning applications.^[6] For example, Zhao et al.’s YOLO+AGAST hierarchical model achieved a 98.5% sunspot recognition rate on HMI continuum images.^[7] However, HMI’s 0.5″ pixel resolution (~360 km on the solar disk) limits its ability to resolve small-scale magnetic activity. For example, magnetic flux tube boundaries with diameters of <150 km (corresponding to angular scales ~0.2″) and microflare current sheets with thicknesses of ~10–50 km remain challenging to observe directly because of the diffraction limit (theoretical value: 1.11″).^[8]

The Optical and Near-infrared Solar Eruption Telescope (ONSET), a cutting-edge ground-based facility independently developed in China, enables multi-dimensional innovation for solar physics via its unique observational modes.^[9] Comprising four vacuum telescope tubes, ONSET employs computer-automated control to acquire quasi-synchronous multi-band solar images across full-disk (~30 arcmin field of view) or high-resolution local (~10 arcmin) regions. Its coverage spans white-light (360.0 ± 1.5 nm and 425.0 ± 1.5 nm), Hα (656.3 ± 0.25 nm), and He I 10830 Å (1083.0 ± 0.4 nm) bands, achieving sub-arcsecond spatial resolution and second-scale temporal resolution^[10]. Its 360-nm near-ultraviolet imaging capability (0.177"/pixel) represents an international breakthrough, filling an observational gap in high-resolution near-UV imaging of the solar photosphere.^{[11, 12]}

Current observational systems exhibit inherent limitations: space-based instruments are constrained by diffraction limits and photon noise, while ground-based observations are susceptible to atmospheric turbulence and temporal discontinuity. Compared with low-resolution images (e.g., SDO/HMI), high-resolution images (e.g., ONSET) typically demonstrate greater pixel density, richer textural detail, and higher reliability. Consequently, solar image resolution enhancement techniques have emerged as a critical approach to overcome the physical constraints of observational instruments. Inspired by super-resolution image reconstruction, these enhancement techniques aim to improve the image quality, enhance fine details, and reduce blurring effects. Super-resolution image reconstruction (SRIR or SR) refers to computational techniques that employ signal and image processing methods to convert low-resolution (LR) images into high-resolution (HR) images.^[13] The fundamental objective involves the recovery of high-frequency details via prior knowledge–guided optimization while preserving critical image information. Current mainstream SR techniques can be categorized into three approaches: (1) interpolation-based methods (e.g., bicubic interpolation) offering computational simplicity but often resulting in edge blurring and detail loss; (2) reconstruction-based approaches (e.g., multi-frame blind deconvolution) requiring accurate point spread function estimation and demonstrating noise sensitivity; and (3) learning-based methods (e.g., SRCNN^[14]) achieving superior reconstruction quality and accommodating complex degradation scenarios. Recent breakthroughs in solar image resolution enhancement have been achieved via deep-learning methods employing end-to-end training paradigms. For example, Muñoz-Jaramillo et al. employed a neural network–based encoder–decoder to elevate MDI and Global Oscillation Network Group (GONG) magnetograms to HMI quality,^[15] integrating ground-based (NSO/GONG) and space-borne (SOHO/MDI, SDO/HMI) data. Li et al. proposed GenMDI, a deep generative model enhancing the temporal resolution of SOHO/MDI line-of-sight magnetograms for active regions.^[16] Deng et al. leveraged generative adversarial network and self-attention mechanisms with 1.6-m Goode Solar Telescope (GST) data to improve HMI’s resolution.^[17]

This study leverages coordinated observations from ONSET (0.177″/pixel) and SDO/HMI (0.5″/pixel) to mitigate the inherent limitations of the individual instruments, achieving simultaneous improvements in the pixel resolution and data utility for enhanced data quality and scientific productivity. We use Level 1 white-light data at 3600 Å from ONSET, collected between January 2022 and November 2022, and dynamically retrieve temporally aligned SDO/HMI continuum observations (time difference ≤ 45 s) via the Fido module in SunPy v3.1, ultimately constructing a cross-platform aligned dataset comprising 6537 matched data pairs. We propose a novel residual local feature–based network architecture, called CISR (Cross-Instrument Super-Resolution), to enhance the pixel resolution of the SDO/HMI continuum data. A comprehensive evaluation and analysis are made to validate its performance. The paper is organized as follows. Section 2 details the preparation of the ONSET–SDO/HMI dataset and elaborates on the CISR algorithm design, network architecture, and training strategy. Section 3 assesses the model’s accuracy and performance using test datasets. Finally, Section 4 concludes with a discussion of the implications of the study and future research directions.

2.   DATA AND METHODS

2.1   Data processing

In deep-learning model training, the scale and quality of the dataset directly influence the model’s generalization capability. Therefore, it is imperative to establish a rigorous data-preprocessing pipeline to enhance the data quality and usability, thereby ensuring the model generalization capability. The preprocessing workflow comprises six main stages.

(1) Data quality control. We performed data quality inspection and integrity checks, removing corrupted, duplicated, and poorly reconstructed samples.

(2) Temporal alignment. Timestamps of the ONSET photospheric data and SDO/HMI continuum data were synchronized to Coordinated Universal Time. Observations were matched within a ±22.5-s sliding window based on the Nyquist sampling theorem:

(3) Data Standardization Processing. The inherent instrumental differences between the ONSET and SDO/HMI systems, including the telescope aperture, seeing conditions, and CCD sampling resolution, result in substantial non-uniformity in their respective feature space distributions. Specifically, the full-disk LR observations from SDO/HMI exhibit multi-dimensional deviations in their scale, contrast ratio, and geometric distortions compared with ONSET’s HR localized imaging, leading to a substantial degradation in cross-platform feature correlations. This nonlinear mapping relationship in the feature space critically constrains both the model interpretability and the quantitative analysis precision. Consequently, prior to image alignment, we implement a multidimensional standardization framework to reconstruct a unified data reference baseline using the following four-step procedure.

(i) Reference Image Coordinate Calibration. The full-disk heliocentric coordinates are translated to the image center based on its FITS header parameters, CROTA2, CRPIX1, and CRPIX2.^[18]

(ii) Limb-Darkening Correction.^[19] A polar coordinate transformation based on the extended full-disk radial median profile is implemented to eliminate the limb-darkening effect in the SDO/HMI images. This ensures consistent grayscale intensity between the solar disk center and the limb regions. Fig. 1A depicts an original SDO/HMI image, while Fig. 1B demonstrates the corrected result following limb-darkening removal.

Figure  1.  Limb-darkening corrected SDO/HMI data.

(A) Coordinate-calibrated SDO/HMI continuum image. (B) SDO/HMI continuum image after limb-darkening correction.

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(iii) Resolution and Scale Normalization (Target Image Downscaling & Blurring). Because the ONSET photospheric data have a 0.177″/pixel resolution and the SDO/HMI continuum data have a 0.5″/pixel resolution, the ONSET target images require trilinear downscaling to one-third their original dimensions, followed by Gaussian kernel blurring for resolution matching with SDO/HMI.

(iv) Grayscale Dynamic Range Optimization. During subsequent SIFT (scale-invariant feature transform) feature detection, input images must be converted from the original 16-bit depth (typical for both ONSET and SDO/HMI) to an 8-bit depth via optimal grayscale windowing. The grayscale threshold is determined using a statistically derived approach based on normal distribution assumptions. Specifically, the threshold range is defined as [μ − 3σ, μ + 3σ], where μ represents the mean pixel intensity and σ denotes the standard deviation. This ±3σ coverage theoretically encompasses 99.7% of the pixel intensity values (following the 3σ principle of normal distributions), thereby enabling effective grayscale segmentation of the solar images. Fig. 2A displays the corresponding 8-bit mapping of the ONSET counterpart after preprocessing, while Fig. 2B illustrates the 8-bit conversion of the preprocessed SDO/HMI image via grayscale thresholding.

Figure  2.  Dynamic range optimization of ONSET 3600-Å images.

(A) 8-bit converted ONSET 3600-Å image via grayscale thresholding. (B) 8-bit converted SDO/HMI image via grayscale thresholding.

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(4) Image Spatial Alignment. This study involves two sets of solar observation images with significant differences: HR local images obtained from ground-based telescopes and full-disk images captured by space telescopes. These datasets exhibit multiple heterogeneous characteristics (as shown in Table 1), including different observation platforms (ground-based versus space-based), temporal acquisition discrepancies, inconsistent working bands, and notable variations in the image scale, intensity distribution, pixel resolution, and viewing geometry. Consequently, we employed a targeted SIFT^[20] algorithm to achieve sub-pixel alignment.

Table  1.  Heterogeneous characteristics of the ONSET and SDO/HMI datasets.

Parameter	ONSET Local Images	SDO/HMI Full-Disk Images	Discrepancy Factor
Pixel Resolution	0.177″/pixel	0.5″/pixel	2.8×
Temporal Resolution	30 seconds/frame	45 seconds/frame	1.5×
Observation Band	3600 Å (White Light)	6173 Å (Continuum)	Δ2573 Å
Field Coverage	10′×10′	Full-disk	Local vs Global
Grayscale Dynamic Range	16-bit (0–65535)	16-bit (0–65535)	—

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(i) Feature point extraction. The extraction process comprises four principal stages: construction of the difference of Gaussian scale space, localization of local extrema, keypoint filtering, and determination of dominant orientations.

(ii) Construction and optimization of local feature descriptors.

(iii) Feature matching optimization based on approximate nearest neighbors. The FLANN^[21] method is employed to accelerate the approximate nearest neighbor search, identifying multiple pairs of matching feature points.

(iv) Determination of geometric transformation parameters. The RANSAC (random sample consensus) algorithm is used as the parameter estimation model. After several iterations, the transformation parameter with the largest set of interior points is finally selected; this is considered to be the best geometric transformation model.

Final image registration with sub-pixel accuracy was achieved via inverse mapping using an affine transformation matrix. Fig. 3 shows the feature point matching between the ONSET partial image and the HMI full-disk image, while Fig. 4 displays the feature point matching in corresponding ONSET–HMI regions.

Figure  3.  Feature point matching diagram between ONSET local images and HMI full-disk magnetograms.

(A) Matched outliers (number of outliers: 5518). (B) Matched inliers (number of inliers: 1099).

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Figure  4.  Feature point matching map of co-aligned ONSET–HMI observation regions.

(A) Matched outliers (number of outliers: 3553). (B) Matched inliers (number of inliers: 650).

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Ultimately, the initial data samples yielded a total of 6537 data pairs after preprocessing and image registration. The HMI continuum data have dimensions of 256 × 256 pixels, while the corresponding ONSET 3600-Å data are sized at 768 × 768 pixels. We allocated the data as follows: training set: 5407 image pairs from January 5 to September 18, 2022; validation set: 590 pairs from October 1 to October 30, 2022; and test set: 540 pairs from November 1 to November 20, 2022.

(5) Variance-Maximized Cropping and Data Augmentation. This procedure consists of (i) randomly extracting 10 128 × 128 candidate regions from full-disk SDO/HMI images; (ii) selecting the sample with the maximum pixel variance from the candidates; (iii) synchronously extracting corresponding 384 × 384 HR regions from ONSET to form training pairs; and (iv) applying random rotations (0°, 90°, 180°, and 270°) and flips to each pair. This design serves two purposes: 1) the variance maximization alleviates class imbalances by prioritizing structurally rich regions and 2) random cropping, rotation, and flipping enhances the data diversity to improve the model generalizability.

(6) Normalization Processing. Prior to network input, all data pairs undergo normalization processing. Because the median (as opposed to the mean) demonstrates superior noise robustness and effectively mitigates interference from extreme bright/dark features in solar images, our normalization method involves dividing each pixel’s original grayscale value by the corresponding image’s median value to obtain the normalized intensity.

2.2   Methods

In recent years, groundbreaking advancements in deep learning, particularly the synergistic evolution of convolutional neural networks (CNNs) and generative adversarial networks, combined with revolutionary improvements in GPU computational power, have significantly advanced SR technology. CNNs play a dominant role in image reconstruction because of their unique local feature extraction mechanisms and the physically interpretable nature of their architectures. In 2012, AlexNet^[22] demonstrated the superiority of CNNs in image feature learning with a significant margin (Top-5 error rate of 15.3% versus 26.2% for traditional methods) in the ImageNet competition. Consequently, this study was developed on the basis of CNN architecture.

2.2.1   Cross-Instrument Solar Image Super-Resolution Model

Single-image SR techniques exhibit substantial domain-specific variations across applications. In natural image processing, models such as EDSR^[23] and RCAN^[24] employ ultra-deep residual networks (e.g., RCAN’s 400-layer architecture) to resolve complex semantic features, including high-frequency textures and multi-scale edges. However, their computational complexity remains prohibitively high, for example, the RCAN model requires 6.3 TFLOPs for 256 × 256 input resolution, rendering them unsuitable for scientific observational data requirements. This study focuses on solar photospheric characteristics, leveraging HR white-light data (3600 Å, 0.177″/pixel) from the ONSET telescope to enhance the resolution of SDO/HMI continuum observations (0.5″/pixel). The core challenges lie in preserving the physical fidelity while optimizing the computational efficiency.

Using systematic preliminary studies, we identified several critical technical insights. First, although expanding receptive fields and increasing network depth can significantly enhance model fitting capability and performance,^[25] the accompanying gradient vanishing/explosion issues require effective suppression via residual structures. We validated the architectural advantages of placing pixel-shuffle operations at the network terminus in image SR tasks; this design not only reduces artificial noise but also enables the model to perform major feature computations in lower-resolution spaces. Further experiments demonstrate that, by constructing more comprehensive feature map receptive fields prior to activation layers and strategically removing redundant activation and convolution layers, we can significantly improve the training stability while maintaining the model performance.

On the basis of the above analysis, this study proposes an improved resolution enhancement network called CISR (Cross-Instrument Solar Image Super-Resolution Model) for the joint reconstruction of multi-instrument solar images to enhance the resolution of SDO/HMI observations (0.5″/pixel). The proposed model was developed on the basis of enhanced residual local feature network (RLFN) architecture originally proposed by Kong et al.^[26], featuring a three-stage processing pipeline for efficient reconstruction: (1) shallow feature extraction: a single 3 × 3 convolutional layer performs the initial feature mapping of the input LR image; (2) deep feature extraction: comprising 12 cascaded residual local feature blocks (RLFBs), where each block contains three Conv-SiLU units (3 × 3 kernel/64 channels) for multi-scale feature extraction, and an efficient spatial attention (ESA) module to expand the receptive field; and (3) image upsampling: 3× upsampling is performed using PixelShuffle^[27] to reconstruct HR images. Fig. 5 shows the complete architecture of the CISR network: the input is an SDO/HMI LR (256 × 256) image and the output is a SDO/HMI SR (768 × 768) depiction enhanced by the network.

Figure  5.  CISR network structure diagram.

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Fig. 6 illustrates the architecture of the ESA module, with the operational pipeline comprising four distinct phases. (1) Channel compression. The ESA module initiates with a 1 × 1 convolution that reduces the input feature channels to 1/4 of their original count, significantly decreasing the subsequent computational load. (2) Multi-scale feature extraction. A stride-2 convolution (halving feature map dimensions to extract high-frequency details) is concatenated with a stride-3 7 × 7 max-pooling operation (generating LR feature maps for large-scale structural information). (3) Lightweight feature reconstruction. The fused features are subjected to lightweight processing through a 1 × 1 convolutional layer, which reduces the number of parameters while preserving the receptive field. Subsequently, the spatial dimensions are restored via bilinear interpolation, followed by element-wise addition. A 1 × 1 convolution is then applied to recover the channel dimensionality, and a spatial attention weight matrix is generated using the sigmoid function. (4) Dynamic feature enhancement. The generated attention weight matrix is element-wise multiplied with the original input features, achieving dynamic reinforcement of the key regions.

Figure  6.  Structural diagram of the efficient spatial attention (ESA) module.

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Compared with the original RLFN architecture, our network incorporates the following key improvements,

(1) Deeper network structure: The number of RLFB modules is increased from 6 to 12 to enhance the feature extraction capability, even though computational resources need to be balanced as a result of the GPU memory constraints.

(2) Expanded channel width: The feature channels are extended from 52 (or 48) to 64, increasing the model’s capacity to capture richer local details.

(3) Activation function optimization: SiLU replaces ReLU, leveraging its smooth nonlinearity to improve the gradient flow in the deep networks, thereby enhancing the high-frequency detail recovery.^[28]

These modifications are based on insights from the original RLFN study^[26] and established deep network design principles, ensuring that the model maintains both efficiency and high accuracy even for more complex tasks.

2.2.2   Loss functions

The loss function serves as a fundamental mathematical tool in deep-learning model training.^[29] It essentially constructs a mapping from the parameter space Θ to a scalar space:

This fundamental tool quantifies the disparity between the predicted outputs and the empirical observations. During the training process, the loss function operates as the primary optimization metric, with its architectural design exerting a dual influence: it governs both the efficiency of the parameter convergence and the physical validity of the resultant model. The backpropagation mechanism leverages this function to determine the gradient descent trajectories, necessitating careful consideration of two critical attributes: precise task objective representation and favorable mathematical properties for stable optimization.

This study fundamentally constitutes an application-driven investigation in high-dimensional nonlinear regression. During systematic experimentation with diverse regression loss functions, we observed that conventional reconstruction-based L2 loss yields visually satisfactory SR reconstructions. However, the linear positive correlation between the L2 gradients and errors, attributed to its continuous and everywhere-differentiable nature, introduces two critical drawbacks.

(1) Error amplification: When the pixel-wise discrepancy between the predictions and ground truth exceeds 1, large-error samples disproportionately dominate the optimization trajectories.

(2) Gradient explosion risk: Unbounded gradient magnitudes incentivize excessive smoothing in output reconstructions as compensation.

Consequently, we implemented L1 loss for the network training. The empirical results demonstrate the superiority of L1 loss over alternatives in both the quantitative metrics and visual assessments. The L1-loss function is not prone to gradient explosion issues and exhibits greater robustness for outliers.

The derivative of the L1 loss is expressed as

However, the L1 loss is non-smooth and non-differentiable at zero, which prevents gradient descent from being properly executed when w = 0. Furthermore, because the derivative of the L1-loss function is constant, the relatively large gradient magnitudes at small loss values may induce model oscillations, thereby impeding convergence.

Building on this foundation, we adopted smooth L1 loss (the Huber loss) to enhance the model performance and training stability by strategically balancing the gradient properties; this method preserves the smooth convergence characteristics of the L2 norm for small errors (|x| < 1) while maintaining the robustness of the L1 norm for large errors (|x| ≥ 1). This design significantly improves the model performance while enhancing both the stability and the generalization capability. Its mathematical formulation is expressed as

The derivative of the smooth L1 loss is given by

The comparison curves of the three loss functions in Fig. 7 show that there are significant differences in the dynamic response characteristics of the three loss functions during the training process. Table 2 shows the performance evaluation results of models trained with different loss functions (L1, L2, and Huber) on the test set, including the average values of three metrics: the pixel-wise correlation coefficient (CC), the peak signal-to-noise ratio (PSNR), and the structural similarity index (SSIM). In detail, the Huber loss achieved optimal results for CC (0.946), PSNR (33.924 dB), and SSIM (0.855), while the L1 loss performed better than the L2 loss for SSIM (0.848 versus 0.837); however, its PSNR (32.924 dB) value was slightly lower than that of the L2 loss (33.287 dB).

Figure  7.  Comparison of L1-loss, L2-loss, and smooth L1-loss (Huber) function curves.

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Table  2.  Performance comparison of the different loss functions (L1, L2, and Huber) on the test set.

Loss	Correlation Coefficient	Peak S/N (dB)	SSIM
L1 Loss (MAE)	0.938	32.924	0.848
L2 Loss (MSE)	0.932	33.287	0.837
Huber Loss	0.946	33.924	0.855

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3.   RESULTS AND DISCUSSION

3.1   Model Training Process

CISR is a deep residual learning–based network architecture for solar image resolution enhancement whose core innovation lies in the integration of multi-scale residual local feature extraction modules with sub-pixel convolutional upsampling mechanisms. The model adopts an end-to-end training paradigm, utilizing Level 1 data from the ONSET telescope as the HR reference (384 × 384) while taking SDO/HMI continuum observation data as the LR input (128 × 128).

The hardware configuration of the experimental platform used in this study consisted of a NVIDIA GeForce RTX 3090 GPU (10,496 CUDA cores, 24GB VRAM).

The training hyperparameter configuration was set as follows. The optimizer employs Adam (β₁ = 0.9, β₂ = 0.999) with an initial learning rate of 0.005, which is dynamically adjusted using ReduceLROnPlateau scheduling (factor = 0.9, patience = 30). The batch training size is set to 32 for optimal GPU memory utilization. The training process implemented early stopping by tracking the validation loss, with training cessation occurring at epoch = 1539.

Figure  8.  Evolution of the smooth L1-loss function throughout the training process. The x-axis represents the training epochs, and the y-axis denotes the smooth L1-loss values. The curve demonstrates stable convergence after approximately 400 epochs.

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As shown in Fig. 9, the data reconstruction performances of two different training datasets are compared. The left, middle, and right columns correspond to the original LR HMI observational data, the CISR algorithm reconstruction results, and the HR ONSET reference data, respectively. A visual analysis reveals that the CISR reconstruction significantly improves the spatial detail representation compared with the original LR HMI data. However, there remains a discernible gap in the texture sharpness and the high-frequency feature fidelity when compared with the true HR observations. (Data dates: 4-20221007T054511_ONSET-20221007_054545_HMI and 5-20221006T065613_ONSET-20221006_065700_HMI).

Figure  9.  Training set performance of the CISR model. From left to right: HMI continuum data (low-resolution, LR), CISR model resolution enhancement result (super-resolution, SR), ONSET photospheric data (high-resolution, HR), and the residual map for two different datasets.

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3.2   Result Evaluation and Analysis

Upon completion of training, the model can be evaluated to examine its performance on the test set. Representative test results are shown in Fig. 10, featuring three characteristic regions: (A) a sunspot, (B) an active region, and (C) a quiet region. For each case, the images displayed from left to right are the original LR HMI continuum data, the SR output from the CISR model, and the corresponding HR ONSET photospheric reference.

Figure  10.  Resolution enhancement results of HMI continuum data using the CISR model.

(A) Original LR HMI data; (B) SR CISR output; and (C) HR ONSET data. The right panels show the intensity profiles along the selected rows, shown by the red lines in panels (A)–(C). (Data dates: 20221102T045521_ONSET-20221102_045615_HMI, 20221111T071214_ONSET-20221111_071245_HMI, and 20221102T074840_ONSET-20221102_074930_HMI).

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Visual inspection reveals that the CISR model effectively restores the fundamental umbra–penumbra structure in both sunspot and active regions, with clearly discernible radial striations in the penumbral filaments, albeit exhibiting slight smoothing effects at transitional boundaries. For quiet Sun regions, it successfully preserves large-scale homogeneous features while significantly enhancing granulation boundaries and suppressing inherent data noise.

To further analyze the resolution enhancement performance of the CISR model, the intensity profile curves were plotted (Fig. 10, right panels). Using the same coordinate system with the pixel position as the horizontal axis and the normalized intensity as the vertical axis, the LR HMI data, SR CISR reconstruction result, and HR ONSET data are represented by blue, orange, and green curves, respectively. The intensity profiles extracted along identical transects for the three test cases provide a quantitative visualization of the model’s reconstruction performance in edge sharpness enhancement, textural feature preservation, and noise suppression efficacy. The results indicate that the CISR reconstruction curve exhibits steeper transitions at sunspot edges, better approximating the ideal sharp features while preserving the amplitude fluctuations of granulation structures; in addition, the reconstruction performance in sunspots and active regions surpasses that in quiet regions, with the results more closely matching the HR images.

Fig. 10 presents a comparative analysis of the model’s reconstruction performance across different solar regions. Using HR images as the ground truth reveals the intricate details present in the actual observations. In the sunspot and active regions, the LR images show significant deviations from the HR images, while the SR results partially compensate for these discrepancies via algorithmic processing, successfully reconstructing key intensity features of the HR images including the umbral intensity depression and the penumbral gradient variations. However, because they are constrained by the current model capabilities and data quality limitations, the SR results do not fully reproduce all of the HR characteristics, exhibiting slight smoothing effects at the umbral boundaries. Profiles from quiet regions demonstrate that SR maintains excellent agreement with HR in the large-scale intensity distributions, although with some attenuation of fine-scale intensity fluctuations.

Fig. 10A, B reveals a significant brightness discrepancy between the LR and HR images at the sunspot centers, which may arise from multiple complex factors including differences in the instrument response functions and radiation transfer effects at different resolutions (particularly point spread function variations). This phenomenon requires further investigation in future work.

The visual comparison in Fig. 10 and the power spectrum analyses in Fig. 11 collectively validate the effectiveness of the CISR model. The results also highlight remaining challenges in boundary detail reconstruction and small-scale feature recovery, providing valuable insights for future model optimization efforts.

Figure  11.  Comparison of the average power spectral lines of LR, SR, and HR for different regions.

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The specific workflow of the average power spectrum analysis method adopted in this paper is as follows. (1) Power spectrum calculation. First, a two-dimensional Fourier transform is performed on each image to compute its logarithmic power spectrum:

Subsequently, the power spectrum is converted to polar coordinates and averaged along the radial direction to obtain a one-dimensional average power spectrum curve. Finally, all of the curves are vertically shifted for normalization to ensure consistent starting points in the low-frequency regime (k→0). (2) Resolution calibration coordinate conversion. The network upsamples the LR HMI images by 3× during resolution enhancement. Consequently, the effective resolution of the reconstructed images becomes 0.5″/3 ≈ 0.167″/pixel. The abscissa is converted to the spatial resolution as follows:

Here, x denotes the pixel coordinates in the image.

The analysis of the average power spectrum in Fig. 11 shows that the reconstructed SR results exhibit significant improvement in the medium-frequency range of 1–3 arcseconds. The SR power spectrum (green curve) aligns more closely with the ONSET reference (blue) than the original HMI data (orange), confirming the method’s effectiveness in enhancing medium-scale structures and substantially reducing the HMI instrumental effects. However, in the high-frequency range (<1.2 arcseconds), the SR power spectrum remains significantly lower than the ONSET reference, indicating an inability to restore the resolution below the diffraction limit. Although the HMI images were magnified by a factor of 3, the sampling below 1 arcsecond actually represents oversampling. This demonstrates that true “super-resolution” was not achieved and that the physical limits were not surpassed, a conclusion we consider scientifically reasonable. No algorithm can create information from nothing.

Fig. 12 presents three corresponding scatterplots comparing the pixel values of the reconstructed results with those of the HR pixel values. The majority of the data points cluster closely around the 1:1 line (the identity line), and the fitted line of all of the scatter points closely coincides with the 45° diagonal, demonstrating high reconstruction fidelity.

Figure  12.  Predicted versus true scatterplot. Pixel-wise agreement between the reconstructed results and the HR data.

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In the resolution enhancement reconstruction task, the absolute residual map and the relative residual map (Fig. 13) reveal the error characteristics of the model from different perspectives. The absolute residual map visually displays the reconstruction deficiencies in the high-frequency details (e.g., edges and textures) via the pixel-wise absolute errors, whereas the relative residual map demonstrates that the model achieves superior reconstruction performance in high-frequency regions with prominent structural features (e.g., sunspots and active regions), where the relative residual values approach zero (corresponding to white areas on the color scale). This observation confirms that the model effectively captures the high-frequency structural features of the solar active regions via the deep feature learning.

Figure  13.  Residual maps for different test datasets. (A) Absolute residuals $(AE=SR-HR)$ between the CISR reconstruction results and the HR ONSET reference data. (B) Corresponding relative residuals$\left(RE=\dfrac{AE}{\left|HR\right|}\right)$. Three distinct test datasets are displayed.

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A quantitative evaluation can be performed using the PSNR, SSIM, and CC metrics. After applying the CISR model to batch-process 540 test datasets (from November 1 to November 20, 2022), we established a statistical quantitative assessment as presented in Table 3. The results clearly demonstrate that the CISR method significantly outperforms both traditional interpolation approaches and SRCNN across all evaluation metrics, confirming the network’s accuracy and applicability for SDO/HMI continuum data enhancement.

Table  3.  Quantitative evaluation table of the statistical results of different methods.

Method	Pixel to Pixel (CC)	Peak S/N (dB)	SSIM
Bicubic	0.862	31.048	0.826
SRCNN	0.93	32.718	0.843
CISR	0.946	33.924	0.855

 | Show Table

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4.   CONCLUSIONS AND FUTURE WORK

This paper presented a cross-instrument resolution enhancement framework (CISR) that synergizes space-based SDO/HMI full-disk observations with ground-based HR ONSET local data to overcome the inherent limitations of single-instrument solar imaging. By establishing a rigorously aligned dataset of 6537 image pairs and developing a lightweight residual local feature block network optimized with smooth L1 loss, we achieved a significant resolution enhancement of the SDO/HMI continuum data (from 0.5"/pixel to 0.167"/pixel). Quantitative evaluations demonstrated CISR’s superiority over traditional methods, with test-set metrics of CC = 0.946, PSNR = 33.924 dB, and SSIM = 0.855. A visual analysis confirmed the model’s capability to improve the solar continuum image resolution while preserving critical photospheric features, including the sunspot penumbral filaments and granulation textures. The proposed variance-maximized cropping strategy and sub-pixel registration pipeline address critical challenges in solar data fusion, enabling robust cross-platform feature alignment even under significant observational heterogeneities (Table 1).

Via a comprehensive analysis, we identified two key limitations in the current CISR model despite its notable advancements. (1) The temporal coverage of the dataset remains insufficient, failing to encompass a complete solar activity cycle, which necessitates further validation of its generalization capability for extreme solar events. (2) The existing evaluation framework predominantly relies on generic metrics such as PSNR and SSIM and lacks specialized assessment criteria tailored to solar physics data characteristics. These two limitations clearly delineate critical directions for future research.

Future work will focus on introducing physics-constrained evaluations to establish a quantitative assessment system based on solar physical properties, thereby enhancing the data reliability, as well as improving the cross-instrument multi-band generalization capabilities to strengthen the model robustness. The cross-instrument data joint reconstruction method proposed in this study provides a feasible pathway for exploring the synergistic optimization of “resolution–coverage–timeliness” in solar physics. This method holds potential for applications in scenarios such as multi-band spectral imaging data collaborative enhancement and may contribute technical experience for future intelligent solar data analysis systems covering broader spectral ranges and multi-scale spatiotemporal domains.