Radio-astronomical Image Reconstruction with Conditional Denoising Diffusion Model

TL;DR

This work addresses the challenge of reconstructing accurate sky models from dirty radio interferometric images, where traditional methods struggle to detect faint sources. It introduces a conditional denoising diffusion probabilistic model that treats dirty images as conditioning input and generates multiple sky-model realizations, enabling uncertainty quantification through aggregation. The authors demonstrate state-of-the-art localization and flux estimation on simulated ALMA-like data, showing substantial improvements over PyBDSF and CLEAN+PyBDSF, particularly at low S/N, and they provide practical measures such as aggregation strategies and a reliability metric. The approach offers a probabilistic, image-to-image translation framework with potential for real-data deployment, though it currently faces speed and transferability considerations that warrant further research.

Abstract

Reconstructing sky models from dirty radio images for accurate source localization and flux estimation is crucial for studying galaxy evolution at high redshift, especially in deep fields using instruments like the Atacama Large Millimetre Array (ALMA). With new projects like the Square Kilometre Array (SKA), there's a growing need for better source extraction methods. Current techniques, such as CLEAN and PyBDSF, often fail to detect faint sources, highlighting the need for more accurate methods. This study proposes using stochastic neural networks to rebuild sky models directly from dirty images. This method can pinpoint radio sources and measure their fluxes with related uncertainties, marking a potential improvement in radio source characterization. We tested this approach on 10164 images simulated with the CASA tool simalma, based on ALMA's Cycle 5.3 antenna setup. We applied conditional Denoising Diffusion Probabilistic Models (DDPMs) for sky models reconstruction, then used Photutils to determine source coordinates and fluxes, assessing the model's performance across different water vapor levels. Our method showed excellence in source localization, achieving more than 90% completeness at a signal-to-noise ratio (SNR) as low as 2. It also surpassed PyBDSF in flux estimation, accurately identifying fluxes for 96% of sources in the test set, a significant improvement over CLEAN+ PyBDSF's 57%. Conditional DDPMs is a powerful tool for image-to-image translation, yielding accurate and robust characterisation of radio sources, and outperforming existing methodologies. While this study underscores its significant potential for applications in radio astronomy, we also acknowledge certain limitations that accompany its usage, suggesting directions for further refinement and research.

Figures (23)

• Figure 1: Simplified pipeline for real and simulated observations. Each pair of antennas collects sky observations that yield UV-visibility data. These data are then aggregated via a gridding process into an aggregated UV grid. Finally, an inverse Fourier transform is applied along with the effect of a primary beam to generate the dirty image.
• Figure 2: Effect of $\gamma$ value on sky model preprocessing. The preprocessing of the sky model via Equation \ref{['eq:normalization']} is significantly affected by the $\gamma$ value. The proposed method modifies the intensities of the image pixels to improve the network's capacity for accurate reconstruction. By employing a nonlinear root operation, nonzero values are pushed closer to one, effectively making the histogram more uniform. However, this modification also impacts the relative distances. Therefore, an optimal $\gamma$ value is required to ensure a compromise between these two tendencies. The histogram y-axis limits are set so that the height of the third bin comprises 80% of the image.
• Figure 3: Schematic representation of diffusion process. The forward process consists in progressively adding noise to the sky model. The inverse process starts with model noise, which is progressively refined with a conditioning on the dirty image.
• Figure 4: Generalized pipeline of proposed method. The top branch represents inference. The DDPM model acts as a stochastic image-to-image translator, transforming the conditioning $\bf z$ and the model noise $\boldsymbol{\epsilon}$ into the target image $\hat{\bf x}_0$ and corresponding $\hat{{\bf s}}$. The predicted sky model is then processed by the localization algorithm, outputting the corresponding coordinates and fluxes. The bottom branch represents the simplified measurement process.
• Figure 5: Schematic representation of training pipeline for time step $t$. The preprocessed sky model ${\bf x}_0$ is corrupted by the DDPM model noise $\boldsymbol{\epsilon}$. The U-Net, given the corrupted target image $\mathbf{x}_{t}$ and conditioned with the dirty image $\bf z,$ tries to estimate the model noise $\hat{\boldsymbol{\epsilon}}$ to denoise the $\mathbf{x}_{t}$. The model is trained to minimize the distance between ${\boldsymbol{\epsilon}}$ and $\hat{\boldsymbol{\epsilon}}$.