U-net Performs 48×48 Blind Deconvolution of Astronomical Images Without Prior PSF Knowledge

Astronomical images are often blurred by the atmosphere and the limitations of telescopes, requiring complex processing to restore clarity. Jean-Eric Campagne of Université Paris-Saclay, CNRS/IN2P3, IJCLab, and colleagues investigate whether a U-Net , a type of artificial neural network , can independently ‘unblur’ these images without needing prior knowledge of the blurring process. This research is significant because traditional deconvolution methods rely on accurate estimations of the point spread function and noise, which are often difficult to obtain. The team simulated realistic astronomical observations and trained the U-Net on these datasets, demonstrating that it not only improves with more training data but also surpasses the performance of conventional Tikhonov deconvolution in difficult scenarios, suggesting a new approach to image restoration in astronomy. Furthermore, their analysis indicates the network learns to adapt to the image geometry, offering insights into its underlying functionality.

Researchers are investigating whether a U-Net, a type of artificial neural network, can independently ‘unblur’ these images without prior knowledge of the blurring process. This research is significant as traditional deconvolution methods rely on accurate estimations of the point spread function and noise, which are often difficult to obtain.

The team simulated realistic astronomical observations using the GalSim toolkit, incorporating random transformations, PSF convolution accounting for both optical and atmospheric effects, and Gaussian white noise. A U-Net model was then trained utilising a Mean Square Error (MSE) loss function, employing datasets ranging in size up to 40,000 images, each with dimensions of 48×48 pixels sourced from the COSMOS Real Galaxy Dataset. Performance was evaluated using Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and cosine similarity metrics, with the latter employed in a two-model comparison.

Experiments revealed the U-Net consistently outperformed the classical Tikhonov deconvolution method, particularly in challenging scenarios characterised by low PSNR and medium SSIM values. The model demonstrated strong generalization capabilities, effectively processing unseen seeing and noise conditions, with optimal performance achieved when validation conditions were included within the training parameters. To investigate the underlying mechanisms driving the U-Net’s success, the study extended its analysis to synthetic Cα images, hypothesising that the network learns a geometry-adaptive harmonic basis, mirroring sparse representations observed in denoising tasks.

This aligns with recent mathematical insights into the adaptive learning capabilities of U-Net architectures, suggesting a deeper understanding of its functionality beyond a simple black-box approach. The innovative methodology employed in this work not only delivers a powerful new tool for astronomical image processing but also provides valuable insights into the potential of deep learning for solving ill-posed inverse problems.

U-Net Deconvolution Restores Simulated Galaxy Images

Scientists achieved significant results in blind astronomical image deconvolution utilising a U-Net model, demonstrating its capacity to function as a standalone end-to-end system without prior knowledge of the Point Spread Function (PSF) or noise characteristics. The research team simulated realistic astronomical observations using the GalSim toolkit, incorporating random transformations, PSF convolution accounting for both optical and atmospheric effects, and Gaussian white noise to create a robust testing environment.

A U-Net model was then trained using a Mean Square Error (MSE) loss function on datasets ranging in size, culminating in a substantial 40,000 images of 48×48 pixels sourced from the COSMOS Real Galaxy Dataset. Performance evaluations, employing metrics such as PSNR, SSIM, and cosine similarity, revealed consistent improvement as the training dataset size increased, with performance notably saturating after 5,000 images. Crucially, cosine similarity analysis between independently trained models confirmed convergence, indicating the stability of the solutions generated by the U-Net.

Experiments demonstrated the U-Net’s ability to outperform the established Tikhonov deconvolution method, particularly in challenging conditions characterised by low PSNR and medium SSIM values, showcasing a remarkable advancement in image restoration techniques. Further tests confirmed the model’s strong generalization capabilities, successfully adapting to unseen seeing and noise conditions, although optimal performance was consistently achieved when validation conditions were included within the training parameters.

Synthetic image experiments support the hypothesis that the U-Net learns a geometry-adaptive harmonic basis, mirroring sparse representations commonly observed in denoising tasks and aligning with recent mathematical insights into the network’s adaptive learning capabilities. These findings suggest the U-Net effectively captures and utilises underlying geometric patterns within astronomical images to achieve superior deconvolution results. The breakthrough delivers a novel approach to astronomical image processing, offering a data-driven alternative to traditional methods reliant on precise PSF and noise modelling.

U-Net Excels at Blind Astronomical Deconvolution

This study successfully demonstrates that a U-Net architecture can perform standalone, end-to-end blind deconvolution of astronomical images without requiring prior knowledge of the point spread function or noise characteristics. Performance consistently improved with increasing training data, eventually reaching a saturation point, and the model notably outperformed a traditional Tikhonov deconvolution method under difficult imaging conditions.

Furthermore, the U-Net exhibited strong generalization capabilities when tested on unseen seeing and noise levels, suggesting robustness beyond the specific training parameters. Analysis indicates the U-Net learns a geometry-adaptive harmonic basis, potentially mirroring sparse representations observed in other image processing tasks, and aligning with recent theoretical work on its adaptive learning capabilities. While the current architecture outputs only the deconvolved image, the authors suggest the learned sparse representation may implicitly contain information about the PSF, opening a promising avenue for future investigation.

The authors acknowledge a limitation in not explicitly estimating the PSF, and propose this as a direction for further research, alongside exploring the model’s applicability to other imaging domains. Measurements confirm the U-Net’s ability to reconstruct finer details and reduce artifacts in simulated astronomical images, potentially unlocking new insights from existing and future telescope data. This work establishes a foundation for future research into deep learning-based deconvolution techniques and their application to a wider range of astronomical challenges.