The primary instrument used in this study is a wide-field computational imaging array developed by our research group. The system consists of ten identical optical telescope units, each equipped with a QHY4040 camera and a 150 mm F/1.15 (D130) lens, and mounted on a simple alt-azimuth array frame (see Figure 1 for photographs of the instrument and observation site). Each unit covers a sky area of approximately 14 ° × 14 °, corresponding to a spatial scale of about 12.3 arcseconds per pixel.

Astronomical imaging acquired from ground-based stations is fundamentally limited by atmospheric turbulence, readout noise, and photon noise, often resulting in raw data frames with low signal-to-noise ratios (SNRs). To improve image quality while addressing the inherent trade-off between model complexity (in terms of parameters and memory) and the large size of wide-field images, a preprocessing stage was applied, focusing on single-frame enhancement and field division (Figure 2).

Initial noise reduction for single-frame images follows standard calibration procedures (Howell, 2006), including subtraction of detector bias, dark current, and flat-field effects, as well as estimation and removal of the sky background. Pixel-by-pixel subtraction of master dark frames effectively suppresses fixed-pattern noise arising from hot pixels and readout processes. This procedure removes discrete bright artifacts caused by spatial variations in dark current (Figure 3), yielding a statistically uniform background. Such background uniformity is critical for improving the accuracy of subsequent centroid estimation and SNR calculation.

To mitigate the conflict between data volume and model complexity, the original 1,600 × 1,600 pixel FITS images were partitioned into smaller subfields. Using a non-overlapping sliding window, each full-frame image was uniformly divided into nine 512 × 512 pixel patches (Figure 4). This strategy serves two purposes: first, the patch size is compatible with the downsampling factors of the U-Net architecture, thereby avoiding interpolation artifacts; second, it substantially reduces the number of parameters required during training, limiting GPU memory usage and reducing overall training time.

Astronomical raw data typically exhibit a high dynamic range, commonly stored in 16-bit format. However, signals from faint targets are often confined to a narrow range of low-intensity values. Direct global normalization would further compress the contrast of these faint objects. The adopted approach therefore combines background subtraction with an adaptive contrast-stretching algorithm, enhancing faint-signal contrast while simultaneously standardizing the dataset and reducing data complexity.

To enhance the effectiveness of the adaptive stretching algorithm in amplifying faint signals, background subtraction is first applied to the images to mitigate the influence of non-uniform backgrounds. Specifically, a tile-based median background estimation method was applied using the photutils package from the Astropy project (Collaboration et al., 2013). Each image is first divided into tiles of 50 × 50 pixels. A spatially varying background model is then constructed by adopting the median statistic (MedianBackground) as the estimator within each tile. The resulting background model is subsequently subtracted on a pixel-by-pixel basis from the original image, yielding a signal frame with the background effectively suppressed.

The background-subtracted frame then undergoes adaptive contrast stretching. The ZScale algorithm implemented in Astropy (Collaboration et al., 2013) is used to automatically determine the optimal display intensity range [ V min , V max ] (Equation 1). Briefly, the algorithm performs random sampling of the input data and employs the median and median absolute deviation (MAD) to reduce the influence of outliers, such as bright stars. An iterative linear fitting procedure with outlier rejection is then applied to determine the final display range. Signal values from the background-subtracted frame ( I n e t ) are clipped to this range (Equation 2), where c l i p   denotes a pixel-value truncation function. This strategy preserves the dynamic range for most pixels while avoiding information loss associated with aggressive clipping. Faint signals are linearly remapped into a wider display range, thereby enhancing their intrinsic contrast features. V min , V max = Z S c a l e I n e t (1) I c l i p = c l i p I n e t x , y , V min , V max (2)

Finally, the processed signal is normalized and exported as an 8-bit grayscale PNG image (Equation 3). P N G i , j = r o u n d 255 × I _ c l i p   i , j − V _ ⁡ min V _ ⁡ max − V _ ⁡ min ⁡ (3)

With respect to the aforementioned enhancement pipeline, analysis of the image grayscale histogram reveals a highly skewed distribution, in which more than 99% of pixel values lie below the upper bound of the 8-bit dynamic range. This result indicates that the majority of the dynamic range is contributed by a small number of high-value pixels, typically associated with bright stars. Furthermore, V _ ⁡ min is statistically defined at a level well below the background mean, ensuring that the clipping operation targets only these extreme outliers. Pixels that are highly unlikely to contain genuine astronomical signal are excluded from the stretching process. For valid faint signals located near or above the background level, subtracting V _ ⁡ min expands subtle intensity differences into tens of gray levels in the 8-bit output image, thereby accentuating the features of faint targets. Therefore, this preprocessing stage does not simply discard information but instead represents a statistically grounded step for feature selection and enhancement. As a result, it provides subsequent deep learning models with input data characterized by enhanced feature clarity and higher contrast.

To quantitatively evaluate the enhancement results, several metrics are employed. The mean gray value (Equation 4) represents the arithmetic average of all pixel intensities and reflects the overall image brightness. Global contrast (Equation 5) measures the dispersion of the intensity distribution, indicating overall contrast strength. Information entropy (Equation 6) characterizes the complexity of the intensity distribution, where x i denotes a pixel gray value, N is the total number of pixels, and p i is the probability of gray level i occurring in the image. x ¯ = 1 N ∑ i = 1 N x i (4) σ = 1 N ∑ i = 1 N x i − x ¯ 2 (5) H = − ∑ i = 0 255 p i ⁡ log 2 ⁡ p i (6)

Applying these metrics to images before and after enhancement yields the comparative results summarized in Table 1. The results indicate that applying ZScale stretching following background subtraction yields increases of approximately 23.53-fold, 17.7-fold, and 3.3-fold in the mean gray value, global contrast, and information entropy, respectively, accompanied by a substantial expansion of the dynamic range and a more effective utilization of the gray-level distribution. Furthermore, incorporating non-uniform background subtraction into the stretching enhancement results in improvements of 1.53% and 14.9% in the mean gray value and information entropy, respectively. A slight decrease in global contrast is observed after background subtraction, which can be attributed to a reduction in overall gray-level dispersion following the removal of non-uniform background components. This behavior is expected and does not hinder the effective enhancement of faint-target contrast. Overall, the proposed pipeline effectively exploits the detailed information of faint targets in compressed images and confirms the effectiveness of background subtraction in improving the performance of adaptive stretching.

Preparation of the label set is a critical step for providing reliable supervisory signals to the deep learning model. An automated label-generation pipeline was developed for the preprocessed images. The pipeline consists of four main steps: background suppression, connected-component segmentation, signal-to-noise ratio (SNR) filtering, and spatial mask encoding. It takes the original single-frame FITS image and the corresponding processed PNG image as inputs and produces a mask image with target annotations suitable for direct use in model training.

To mitigate the influence of dark current and fixed-pattern noise, candidate targets are initially extracted using a threshold-based segmentation criterion (Equation 7): T x , y = B x , y + f · σ B , f = 0.5 (7) where σ B denotes the background standard deviation and f is an empirical scaling factor. As this step is intended as a preliminary extraction stage designed to retain as many potential targets as possible for subsequent filtering, f is conservatively set to 0.5. Connected-component labeling is then applied to the resulting binary image, after which regions containing fewer than two pixels are automatically discarded. This step ensures that only physically plausible source blobs are retained for further analysis.

To prevent undetectably faint targets from contaminating the training set, the pipeline applies an explicit SNR-based threshold filter (11). The SNR calculation strictly follows the aperture photometry framework to maintain consistency with standard astronomical measurement practices. For each source blob identified from the connected components, a bounding circular aperture radius R is first calculated (Equation 8): R = max i P i − c 2 + 1 , c = P (8) where P i denotes the spatial coordinate of the i -th pixel and c represents the centroid. One pixel is added to the calculated radius to ensure that the aperture fully encloses the target signal. Using this radius to define a circular aperture, the total net signal in electron units within the aperture is computed (Equation 9): F e = F A D U − A · μ B · G (9) where F A D U is the total Analog-to-Digital Unit (ADU) count within the aperture, A is the aperture area in pixels, μ B is the mean background level estimated from a concentric sky annulus, and G is the camera gain (e⁻/ADU). Background fluctuations are estimated within the same sky annulus, yielding the per-pixel background variance σ B 2 . According to standard error propagation in aperture photometry, the expected background noise in electron units is given by Equation 10: σ b g = A · σ B · G (10) where σ B is the standard deviation measured in the background annulus. The target signal-to-noise ratio is then calculated in the standard form used in aperture photometry (Equation 11): S N R = F e F e + σ b g (11)

Which accounts for both source photon noise and background Poisson noise, consistent with theoretical models used in mainstream photometry software. Furthermore, to accurately anchor the celestial coordinates of real targets, the Gaia DR3 catalog (Vallenari et al., 2023) is used as a reference, with its sub-milliarcsecond-precision positions mapped to image pixel coordinates. Because the detection limit of Gaia DR3 (G ≈ 20.7 mag) is deeper than that of the observational images, many faint cataloged sources have fluxes below the background noise level and therefore do not form distinct connected components. To construct a reliable training label set, the detectability of each Gaia source is assessed directly in the images. Specifically, fixed 3 × 3 pixel aperture photometry is performed at the mapped pixel position of each source, and the corresponding SNR is calculated. This aperture size is approximately twice the full width at half maximum (FWHM) of the point spread function (PSF) measured in the images, ensuring that it fully encloses a point source. Finally, only sources with an SNR ≥2.0 are retained as valid training labels. This threshold was selected to preserve as many detectable astronomical objects as possible while maintaining a one-to-one correspondence with the training labels (Figure 5).

This study develops an astronomical image segmentation model based on the U-Net architecture (Ronneberger et al., 2015), which is further adapted to meet the specific requirements of faint astronomical target detection (Figure 7).

The conventional U-Net architecture employs paired 3 × 3 convolutional operations at each layer, resulting in an effective receptive field of only 5 × 5 after stacking. For faint targets, whose informative content is often confined to only a few pixels, this receptive field—although sufficient to encompass the target itself—provides limited contextual information for discriminating genuine sources from background noise. To address this limitation, we design a multi-branch Feature Enhancement Module (FEM). This module adopts a parallel architecture, incorporating both a standard 3 × 3 convolutional branch and a 5 × 5 depthwise separable convolutional branch. These branches are designed to capture fine-grained local features and broader contextual information, respectively. The extracted features are subsequently fused using a 1 × 1 convolution, enabling effective multi-scale feature integration and enhancing the network’s representational capacity for faint targets. Furthermore, the use of depthwise separable convolution enables dual receptive fields while substantially reducing the parameter count associated with the 5 × 5 kernel, thereby improving training efficiency and generalization performance.

In contrast to the three-channel input used in the original U-Net, the proposed model adopts a single-channel input to better accommodate astronomical grayscale imagery. The encoder follows the canonical U-Net hierarchical downsampling scheme, employing max-pooling operations and double-convolution blocks. Each block consists of two consecutive 3 × 3 convolutional layers that serve as the fundamental feature extraction unit. The input image first passes through an initial double-convolution block to extract low-level feature representations. Each subsequent downsampling stage halves the feature-map resolution using a 2 × 2 max-pooling operation, followed by a double-convolution block that doubles the number of output channels (64 → 128 → 256 → 512), forming a four-stage encoding path. This design reduces computational cost while preserving critical edge information. Skip connections forward feature maps from each encoder level directly to the corresponding decoder level, providing high-resolution structural priors for the upsampling path.

In the decoder, bilinear interpolation–based upsampling is employed to mitigate checkerboard artifacts. Which smoothly enlarges feature maps by computing weighted averages of neighboring pixels. The upsampled features are concatenated channel-wise with the corresponding encoder features through skip connections, and the resulting feature map is subsequently processed by a double-convolution block. This process is repeated at each decoding level, progressively restoring spatial resolution and ultimately producing the final segmentation map.

Furthermore, the symmetric structure of U-Net, in which the encoder and decoder comprise an equal number of layers, is essential to its performance. This symmetry enables skip connections to merge feature maps at corresponding spatial scales, allowing high-resolution information from early encoder stages to compensate for detail loss incurred during downsampling. As a result, multi-scale feature fusion is achieved, significantly enhancing overall segmentation accuracy.

This study constructs a dedicated dataset for astronomical target recognition using real observational images acquired with the same telescope system. To enable a rigorous assessment of the deep learning model’s generalization capability and to minimize overfitting, the dataset is constructed such that the sky regions covered by the training and testing data are strictly isolated. The complete dataset comprises 20 images, which are divided into two mutually exclusive subsets in terms of sky coverage: 8 images for training and validation, and 12 images reserved as an independent test set. The observational parameters of key reference images are summarized in Table 2 for quantitative analysis. The field center coordinates of the final image in the training phase and the first image in the testing phase (Figure 8) are (RA, Dec) = (300.76°, −5.90°) and (308.86°, −5.91°), respectively. These values indicate that, following completion of the training observations, the telescope pointing was deliberately adjusted for the test set, resulting in a substantial right ascension offset of approximately 8.09°. Based on the system optical parameters—focal length FL = 124.9 mm and pixel size Pscale = 0.0090 mm—the resulting image scale is approximately 14.86 arcsec pixel^-1. With an effective imaging area of 1800 × 1800 pixels, the corresponding field of view has a width of approximately 7.4° and a diagonal of about 10.5°. Under these conditions, an RA offset exceeding 8° ensures that the projected sky areas of the two fields are completely separated. Specifically, the RA coverage of sky region A spans approximately 297.06°–304.46°, while that of sky region B spans approximately 305.16°–312.56°. A gap of approximately 0.7° exists between the two regions, ensuring the absence of any sky overlap.

Based on the observational images described above, each full-frame image was partitioned into subfields, yielding a total of 180 subfield images with a resolution of 512 × 512 pixels. For the first 8 images, subfields 1, 3, 4, 6, 7, and 9 were combined to form the training set, while subfields 2, 5, and 8 were used as the validation set for hyperparameter tuning. All subfields derived from the remaining 12 images were reserved as an independent test set to evaluate model performance on entirely unseen data, including potential observational variations.

The dataset was annotated using the Gaia catalog, resulting in approximately 208,095 labeled stellar point-source targets. The model was implemented using the PyTorch framework and trained on an NVIDIA GeForce RTX 4060Ti GPU.

To systematically assess the performance of the proposed ATD-DL framework, we compare it against two widely used traditional astronomical detection tools: SExtractor and DAOPHOT (specifically its DAOFind module). This evaluation follows established practices for benchmarking astronomical detection methods. Precision, Recall, and F1-score were computed consistently across all 108 test images, which contain approximately 87,000 true sources. Because traditional methods rely on manually specified detection thresholds, a dense parameter scan was first conducted: thresholds from 0.5 to 2.0 for SExtractor and from 4.0 to 8.0 for DAOFind, both in steps of 0.1. Subsequently, ten representative parameter points were selected for each method based on the Precision–Recall criterion (Table 3). The remaining primary parameters used for SExtractor are listed in Table 4, with SEEING_FWHM selected as the optimal value through fine-tuning and comparative testing on real images. For deep learning–based target detection, StarNet (Xue et al., 2020) and DNA-Net (Li et al., 2023) were selected for comparison with the proposed method, and ten checkpoints saved during training were used for each model.

Under identical test conditions and hardware settings, the comparison sequence shown in Figure 11 uses ten nodes along the horizontal axis to represent progressively increasing detection thresholds for the traditional methods, which simultaneously reduce both detection and false-alarm rates. A systematic comparison of the overall performance trends is conducted in terms of precision, recall, and F1-score. The analysis focuses on quantifying performance gains using the mean of the three data points with the highest F1-scores (Figure 12), and on comparing the magnitude of these gains across different signal-to-noise ratio (SNR) intervals (Figure 13).

As shown in Figure 11, a modest increase in the detection threshold for SExtractor initially leads to a rapid rise in precision accompanied by only a minor decrease in recall, resulting in a peak F1-score. In contrast, the deep learning–based methods maintain consistently higher average levels of both precision and recall than the two traditional approaches. To evaluate detection robustness (Figure 12), the three data points with the highest F1-scores for each method were selected and averaged. The deep learning approach exhibits more stable performance across all metrics compared with traditional methods. Detailed metric values at peak F1-score performance for each method are listed in Table 5. Furthermore, to facilitate a fair comparison of detection capability across methods, thresholds for traditional approaches and parameter settings for deep learning models were selected to yield a Precision of approximately 90%. Under these matched Precision conditions, detection performance for faint targets (2 < SNR <5) was compared. As shown in Table 5, ATD-DL achieves a higher recall for faint targets (54.93%) than DNA-Net (48.99%), StarNet (45.83%), SExtractor (36.11%), and DAOFind (1.81%), demonstrating its superior sensitivity in the low-SNR regime.

To assess the ability of the models to detect extremely faint targets, the recall rate was computed within fine SNR bins of width 1 for each model at its maximum F1-score (Figure 13). Compared with traditional methods, the performance advantage of ATD-DL increases steadily toward lower SNR values, rising from approximately 3% for sources with SNR >10 to about 20% for sources in the SNR three to four bin. Although DNA-Net and StarNet exhibit detection performance comparable to ATD-DL in high-SNR regimes, ATD-DL shows a marked improvement for SNR values below 5. This indicates that a substantial fraction of the overall performance gain of ATD-DL arises from its enhanced ability to recover the faintest detectable targets.

Under identical optimal F1-score conditions, the astrometric positioning accuracy of the proposed method was further evaluated. Gaia DR3 catalog coordinates were first projected into the image plane using the instrument plate model to serve as reference positions. The predicted catalog was then cross-matched with the reference catalog using a 2-pixel matching radius, yielding matched source pairs. Coordinate residuals in the image plane were calculated for each pair, and their mean was taken as the systematic bias. After subtracting the corresponding directional bias, the remaining residuals were used to compute the root mean square (RMS) error in each direction. Based on the system optical parameters—focal length FL = 124.9 mm and pixel size Pscale = 0.0090 mm—the telescope image scale is approximately 14.86 arcsec pixel^-1.

The evaluation results presented in Table 6 indicate that the proposed method exhibits a clear advantage in astrometric positioning accuracy. The total RMS error achieved by ATD-DL is 0.2247 pixels (3.3385 arcseconds), corresponding to reductions of 43% and 27% relative to the traditional methods SExtractor (0.3946 pixels, 5.8640 arcseconds) and DAOFind (0.3080 pixels, 4.5765 arcseconds), respectively. ATD-DL further attains the lowest RMS errors in both the X and Y directions among the three methods considered. In addition, DNA-Net and StarNet do not explicitly address precise source centroiding in their original formulations. Accordingly, the same weighted-average centroiding strategy adopted by ATD-DL was also applied to these models for consistency. Under the constraints of this centroiding approach, all three segmentation-based deep learning models yield comparable centroiding accuracy. Nevertheless, the results indicate that deep learning–based approaches generally provide higher positioning accuracy than traditional methods, particularly when operating near the faint detection limit.

In summary, although traditional methods can improve Precision by increasing detection thresholds, this gain is accompanied by a rapid loss in Recall. In contrast, the deep learning approach preserves sensitivity to faint target features, achieving a more favorable balance between detection completeness and false-alarm suppression, particularly near the detection limit.

To rigorously assess the effectiveness of the proposed Feature Enhancement Module (FEM), a dedicated ablation study was conducted. The baseline model adopted a standard U-Net architecture, in which the first encoder layer employed a conventional 3 × 3 double-convolution block. To avoid masking improvements in faint-target detection by aggregate performance metrics, a more targeted evaluation strategy was adopted, focusing exclusively on detection counts for faint targets with signal-to-noise ratios (SNR) between 2 and 5. To eliminate the influence of differing Precision levels, five parameter sets with closely matched Precision values were selected for comparison between the baseline U-Net and the enhanced model (UNet + FEM). The corresponding results are summarized in Table 7.

The results show that, while maintaining comparable overall Precision (for example, 97.49% for U-Net and 97.50% for UNet + FEM in parameter set 1), the enhanced model yields a pronounced increase in the number of detected faint targets across all comparisons. Notably, even under highly conservative operating conditions with Precision exceeding 99%, the FEM preserves strong sensitivity to faint sources. In particular, for parameter set 5, the number of detected faint targets is approximately doubled. These results demonstrate that the FEM effectively enhances the model’s ability to learn and recognize faint-target features without compromising overall detection accuracy, thereby substantially improving faint-source recovery.

SExtractor provides both source positions and segmentation masks, a functionality analogous to the output of the proposed model. To investigate the underlying causes of the observed performance differences, a comparative analysis was performed between the segmentation maps generated by SExtractor (SEGMENT) and those produced by ATD-DL.

SExtractor relies on classical threshold-connected segmentation. As illustrated in Figure 14, when the detection threshold is lowered to recover fainter sources, the resulting segmentation masks for bright targets become increasingly diffuse. Mask contours become strongly perturbed by background noise, leading to substantial centroid shifts that may ultimately produce false positives. In contrast, the encoder–decoder architecture of ATD-DL integrates multi-scale contextual information by formulating semantic boundary localization as a pixel-wise classification task. As a result, the segmentation masks exhibit low dispersion during centroid extraction. For brighter, high-SNR targets, mask boundaries remain stable across different operating points (conservative high-precision estimation versus optimistic high-completeness estimation), with performance differences arising mainly from the recovery of additional faint, low-SNR targets (Figure 15).

To further illustrate the effect of lowering SExtractor’s detection threshold in pursuit of increased faint-source recovery, the same centroid extraction procedure used for ATD-DL was applied to SExtractor outputs. As shown in Table 8, when the detection threshold is reduced below 0.5, Recall decreases rather than improves. This behavior arises because excessively low thresholds cause segmentation masks to over-expand, shifting centroids to such an extent that otherwise correctly segmented targets are assigned incorrect coordinates and are subsequently missed during the cross-matching process. Although this effect is also present at higher thresholds, it is partially obscured by the increased number of newly detected faint sources.

Visual inspection of the segmentation masks at optimal F1 performance (Figure 15) indicates that SExtractor tends to overestimate the spatial extent of bright sources, frequently merging adjacent faint targets into a single connected component. This behavior substantially limits its ability to individually segment faint objects. In contrast, ATD-DL produces segmentation masks that are both more faithful to the underlying sources and more stable.

In summary, the threshold-connected segmentation mechanism employed by SExtractor suffers from excessive bright-source area expansion and limited separation of faint targets when operating near the detection limit, leading to deteriorating performance at lower thresholds. By contrast, ATD-DL benefits from low-dispersion segmentation masks produced by the deep learning model and superior sensitivity to low-SNR targets, maintaining high centroid accuracy. The method consistently outperforms SExtractor across all key metrics, demonstrating a clear advantage in the combined task of target segmentation and centroid extraction. It consistently outperforms SExtractor across all key metrics. This analysis elucidates the primary factors underlying the superior performance of ATD-DL in astronomical target detection.