Blind Deconvolution in Astronomy: How Does a Standalone U-Net Perform?

TL;DR

This work investigates whether a standalone U-Net can achieve end-to-end blind deconvolution of astronomical images without explicit PSF or noise priors. Using GalSim-based simulations of realistic galaxy observations, the authors train a compact U-Net and evaluate its performance across training-set sizes, comparing it to a non-blind, oracle-like Tikhonov method. They find that performance substantially improves with data, saturating around 5,000 training images, and that two independently trained U-Nets converge to similar solutions, indicating stability. The U-Net can match or outperform Tikhonov in challenging conditions and generalizes to unseen seeing and noise patterns, suggesting it learns adaptive sparse representations (geometry-adaptive harmonic bases) that enable effective blind deconvolution of small astronomical patches. The results point to a promising, data-driven approach for end-to-end blind deconvolution in astronomy and motivate further theoretical and architectural explorations, including larger datasets and transformer-based variants.

Abstract

Aims: This study investigates whether a U-Net architecture can perform standalone end-to-end blind deconvolution of astronomical images without any prior knowledge of the Point Spread Function (PSF) or noise characteristics. Our goal is to evaluate its performance against the number of training images, classical Tikhonov deconvolution and to assess its generalization capability under varying seeing conditions and noise levels. Methods: Realistic astronomical observations are simulated using the GalSim toolkit, incorporating random transformations, PSF convolution (accounting for both optical and atmospheric effects), and Gaussian white noise. A U-Net model is trained using a Mean Square Error (MSE) loss function on datasets of varying sizes, up to 40,000 images of size 48x48 from the COSMOS Real Galaxy Dataset. Performance is evaluated using PSNR, SSIM, and cosine similarity metrics, with the latter employed in a two-model framework to assess solution stability. Results: The U-Net model demonstrates effectiveness in blind deconvolution, with performance improving consistently as the training dataset size increases, saturating beyond 5,000 images. Cosine similarity analysis reveals convergence between independently trained models, indicating stable solutions. Remarkably, the U-Net outperforms the oracle-like Tikhonov method in challenging conditions (low PSNR/medium SSIM). The model also generalizes well to unseen seeing and noise conditions, although optimal performance is achieved when training parameters include validation conditions. Experiments on synthetic $C^α$ images further support the hypothesis that the U-Net learns a geometry-adaptive harmonic basis, akin to sparse representations observed in denoising tasks. These results align with recent mathematical insights into its adaptive learning capabilities.

Figures (13)

• Figure 1: Example of a naive deconvolution of HST image using the associated HST PSF.
• Figure 2: Example of an optical PSF (zoom $\times 3$) obtained from galsim.OpticalPSF.
• Figure 3: Examples of effects of atmospheric seeing (the FWHM of Kolmogorov function is noted atm) on the optical PSF shown on Figure \ref{['fig:psf_atm_exemple']}.
• Figure 4: Examples of U-Net deconvolution (see text).
• Figure 5: Left: PSNR of deconvolved images as a function of the PSNR of the observed images. The color gradient of the data points, ranging from light blue to black, distinguishes U-Net models trained with increasing sizes of the training dataset ($N=100$, $N=500$, $N=1000$, $N=5000$, $N=10000$, $N=20000$, and $N=40000$). The error bars represent the standard error on the mean in each bin of the profile histogram. Right: same legend but considering the SSIM metric. In each subfigure, the dashed line represents the case where the PSNR (or SSIM) of the deconvolved images is equal to the PSNR (or SSIM) of the observed images.