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Comparative Evaluation of Restoration Schemes as Preprocessing for Deep Learning Detection and Deblending of Astronomical Point Sources in Ground-Based Optical Imaging Systems

This study demonstrates that applying model-based restoration techniques, specifically Richardson–Lucy and maximum a posteriori methods, as preprocessing significantly enhances the ability of deep learning models to detect and deblend faint, closely spaced astronomical point sources in ground-based optical images, even when traditional reconstruction quality metrics do not fully reflect these detection gains.

Original authors: Erysso Boukouvala, Maria Barbarosou

Published 2026-09-01

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CC BY 4.0

Original authors: Erysso Boukouvala, Maria Barbarosou

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast, crowded neighborhoods of the night sky, stars often appear so close together that they blur into a single, glowing smudge. For astronomers trying to map the universe, this blurring is a significant obstacle. When two stars are separated by a distance smaller than the natural blur of a telescope's view, their light overlaps, making it difficult to tell if there is one bright star or two distinct ones. This problem is compounded by the fact that one star might be much dimmer than the other, causing the fainter companion to hide in the bright glare of its neighbor. To solve this, scientists have long relied on mathematical techniques to reverse the blurring, a process known as image restoration, hoping to sharpen the view before they begin counting stars. However, a new question has emerged: does sharpening the image first actually help modern computer programs, which are now trained to find these stars automatically, or does the extra processing step confuse them?

A team of researchers at the Hellenic Air Force Academy set out to answer this question by creating a massive, controlled experiment using computer-generated images of the sky. They did not use real telescope photos, which often lack a perfect "answer key" to verify if a star was truly missed or hidden. Instead, they built a digital simulation of a ground-based optical telescope, complete with a realistic model of how the atmosphere blurs starlight, how the camera sensor captures light, and how random noise interferes with the signal. They generated 1,000 synthetic images, each containing between 8 and 25 simulated stars. Crucially, they included thousands of pairs of stars that were extremely close together, some separated by as little as 3 pixels on the screen, and some with brightness differences as extreme as 30 to 1. Because they created these images themselves, they knew the exact number, position, and brightness of every single star, giving them a perfect ground truth to measure success against.

The researchers then tested five different ways of preparing these images before feeding them into two different types of artificial intelligence networks designed to detect the stars. The first method was to use the raw, blurry images exactly as they were. The other four methods involved applying different mathematical restoration techniques to the images first. These included a classic linear filter, a method that iteratively refines the image based on light statistics, and two variations of a more advanced technique that uses a mathematical rule to encourage the image to look like a collection of sharp, isolated points rather than a smooth blur. The goal was to see if cleaning up the image beforehand made the computer's job easier, harder, or made no difference at all.

The results were clear and pointed toward a specific strategy. The artificial intelligence networks performed significantly better when they were given images that had been processed by the more advanced restoration methods, particularly the one that encouraged sharp, isolated points and the iterative statistical method. In the most difficult scenarios—where stars were faint and packed tightly together—the networks using these restored images found many more stars than the networks looking at the raw, blurry pictures. For instance, in the tightest groupings with the faintest stars, the best restoration methods helped the computer find roughly twice as many stars as it could find on its own. This improvement held true even when the two different computer network designs were tested, suggesting that the benefit comes from the quality of the image itself, not just from a specific type of computer program.

Perhaps the most surprising discovery was that the quality of the restored image, measured by how closely it matched the original perfect simulation, did not tell the whole story. One of the best-performing restoration methods produced images that, by standard mathematical measures of error, looked less perfect than images produced by other methods. Yet, when these "imperfect" images were given to the star-finding computer, it found more stars and resolved more close pairs than it did with the "more perfect" images. This suggests that for the specific task of finding stars, having a slightly blurry but correctly centered peak of light is more useful than having a mathematically perfect but slightly shifted or diffuse image. The study concludes that for the difficult job of spotting faint, crowded stars, using these specific restoration techniques as a first step before letting a computer do the counting is a powerful and effective strategy, turning a nearly impossible task into a solvable one.

Technical Summary: Comparative Evaluation of Restoration Schemes for Deep Learning Detection of Astronomical Point Sources

Problem Statement
Detecting closely spaced astronomical point sources (e.g., binary stars or blended catalogue entries) is a persistent challenge in ground-based optical imaging. When the separation between sources approaches the system's effective Point Spread Function (PSF) width, their profiles overlap significantly. In such scenarios, particularly at low signal-to-noise ratios (SNR), the fainter member of a pair is often lost within the wings of the brighter source. While image restoration and automated source detection are complementary stages in the astronomical imaging pipeline, there is a lack of controlled, systematic comparisons regarding how different classical and model-based restoration methods influence the performance of independently trained Convolutional Neural Network (CNN) detectors. Furthermore, it remains unclear whether improvements in conventional image reconstruction quality metrics (such as pixel-wise error) translate directly into gains in source detection and pair-resolution capabilities.

Methodology
The study employs a controlled synthetic dataset to evaluate five distinct input conditions for CNN-based detection:

Unrestored images (Baseline).
Wiener filtering.
Richardson–Lucy (RL) deconvolution.
Maximum A Posteriori (MAP) restoration (unregularized, $\lambda=0$ ).
Sparsity-regularized MAP restoration ( $\lambda=0.01$ ).

Dataset and Forward Model:
The dataset consists of 1,000 synthetic $128 \times 128$ pixel images containing 16,613 simulated stellar sources, including designated close pairs with separations of 3–5 pixels. The forward observation model simulates a ground-based optical system using a Moffat PSF (FWHM = 3.5 px), finite pixel sampling, a Poisson-Gaussian noise model (photon noise + Gaussian read noise), and a spatially uniform sky background. A purpose-built generator was used to ensure precise control over pair separations and flux contrasts (up to 30:1), providing exact ground truth for quantitative evaluation.

Restoration Techniques:

MAP Restoration: Utilizes a shifted-Poisson approximation to handle the mixed Poisson-Gaussian observation model. It incorporates an $\ell_1$ sparsity prior to promote localized flux peaks and a non-negativity constraint. Optimization is performed via proximal-gradient descent.
RL Deconvolution: A classical iterative method targeting the unregularized maximum-likelihood solution under a pure Poisson model, serving as a baseline for the MAP formulation without Gaussian noise correction or sparsity penalties.
Wiener Filtering: A linear, non-iterative baseline using a parametric noise-to-signal ratio.

Detection Framework:
Two distinct CNN architectures were trained independently for each input scheme under a five-fold cross-validation protocol:

Residual CNN: A compact network with residual blocks and approximately 112k trainable parameters.
Compact U-Net: An encoder-decoder architecture with skip connections and approximately 467k trainable parameters.

Both networks were trained to regress a target heatmap (Gaussian peaks at source locations) using Mean Squared Error (MSE) loss. Detection performance was evaluated using precision, recall, F1-score, and a strict "pair-resolution rate" (requiring distinct detection of both components in a close pair).

Key Results

Overall Performance: Across both architectures, MAP and RL inputs consistently achieved higher recall and F1 scores compared to unrestored and Wiener-filtered inputs. The Residual CNN achieved mean F1 scores of 95.70–95.95% for MAP/RL inputs versus 92.95–93.05% for unrestored/Wiener inputs. The U-Net showed similar trends, though it performed better on the unrestored baseline than the Residual CNN did.
Flux and Separation Dependence: The benefits of restoration were most pronounced for faint sources ( $F < 250$ counts) at small separations ( $[3, 4)$ px). For the most challenging category ( $F < 150$ , separation $[3, 4)$ px), RL improved recall from 13.8% (unrestored) to 33.9% for the Residual CNN.
Pair Resolution: Restoration significantly improved the resolution of close pairs, particularly in high-contrast regimes. For pairs with separation $[3, 4)$ px and flux contrast $4 \le C < 10$ , RL increased the pair-resolution rate from 37.3% (unrestored) to 71.8% (Residual CNN). Even in the extreme regime ( $C \ge 10$ ), restoration methods recovered a substantially larger fraction of pairs than the baseline.
Reconstruction Quality vs. Detection Utility: A critical finding is that pixel-wise reconstruction quality metrics (specifically Normalized Mean-Squared Error, NMSE) do not fully predict detection utility. MAP restorations exhibited relatively high NMSE due to incomplete peak sharpening (energy distributed over neighboring pixels), yet they supported CNN detection performance competitive with RL. This suggests that task-specific metrics are necessary when restoration is used as preprocessing for detection.

Significance and Claims
The paper claims that classical and model-based restoration methods (specifically MAP and RL) can effectively enhance CNN-based detection and deblending of faint, closely spaced astronomical point sources. The study demonstrates that:

Preprocessing Value: Restoration is not merely a reconstruction task but a valuable preprocessing stage that improves the detectability of sources that are otherwise lost in PSF overlap and noise.
Architecture Independence: The observed benefits of restoration are robust across different network architectures (Residual CNN and U-Net), suggesting the gains are inherent to the input data quality rather than specific to a single detector design.
Metric Divergence: Conventional image-quality metrics (like NMSE) are insufficient for evaluating restoration pipelines intended for source detection. Task-specific metrics (recall, pair-resolution) reveal performance improvements that pixel-wise error metrics may obscure.
Operational Regimes: The study identifies specific regimes (low flux, small separation, high contrast) where restoration provides the most significant operational value, transitioning difficult detection problems into moderate or high-recovery scenarios.

The authors conclude that while the synthetic design involves controlled simplifications (e.g., spatially invariant PSF), the results provide strong evidence for the utility of restoration preprocessing in crowded-field optical imaging systems.

Technical Summary: Comparative Evaluation of Restoration Schemes for Deep Learning Detection of Astronomical Point Sources

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