Radio-Interferometric Image Reconstruction with Denoising Diffusion Restoration Models

TL;DR

The paper tackles the ill-posed problem of reconstructing radio-sky images from incomplete visibilities by learning a data-driven prior on radio galaxies with a denoising diffusion probabilistic model and applying Denoising Diffusion Restoration Models to sample posterior reconstructions under the measurement process. It integrates the measurement model $\mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{z}$ with a learned prior, and demonstrates telescope-agnostic reconstruction across simulated VLA, EHT, and ALMA configurations, achieving PSNRs exceeding 60 and outperforming CLEAN and conditional DDPM baselines. Key contributions include a memory-efficient SVD-based DDRM procedure for radio interferometry, unconditional diffusion priors trained on real radio-galaxy data, and a quantitative comparison showing superior MSE and PSNR metrics. The work has practical significance for robust, physics-consistent radio-imaging in surveys and multi-telescope campaigns, enabling high-fidelity reconstructions without array-specific retraining; future work covers uncertainty calibration and extension to more complete forward models (e.g., W/A-terms) and larger image sizes.

Abstract

Reconstructing images of the radio sky from incomplete Fourier information is a key challenge in radio astronomy. In this work, we present a method for radio interferometeic image reconstruction using a data-driven prior for the radio sky based on denoising diffusion probabilistic models (DDPMs). We first train a DDPM on radio galaxy observations from the VLA FIRST survey. We create simulated VLA, EHT, and ALMA observations of radio galaxies, then use an unsupervised posterior sampling method called Denoising Diffusion Restoration Models (DDRM) to reconstruct the corresponding images, using our DDPM as a prior. Our approach is agnostic to the measured radio interferometric data and naturally incorporates the physics of the measurement process. We are able to reconstruct images with very high fidelity PSNR>60, a marked improvement over CLEAN and similar image reconstruction methods using conditional DDPMs

Figures (5)

• Figure 1: Neural Network Architecture used for the DDPM network.
• Figure 2: A selection of radio galaxies from the test dataset.
• Figure 3: Diagram of sampling matrix $\mathbf{S}$, dirty beam $\mathcal{F}^{-1}\mathbf{S}$, true image$\mathbf x$, dirty image $\mathbf x_D = \mathcal{F}^{-1}(\mathbf{S})*\mathbf x$ for the three telescopes considered in this work.
• Figure 4: Reconstruction results for 4 example radio glaxies from the test data set using a simulated VLA observation. Columns from left to right are: the true image $\mathbf{x}$, the dirty image $\mathbf{x}_D$, the CLEAN restored image, the residual between the clean image and the true image, the DDRM reconstructed image, the residual between the DDRM image and the true image, the mean DDRM image, the per-pixel standard deviation map, and the SRE. The plots in the last three columns are calculated across 128 DDRM reconstructions.
• Figure 5: Histogram of the Mean Squared Error (MSE) distributions for CLEAN and DDRM reconstructions. DDRM consistently reconstructs images with better MSE compared to CLEAN.