  In radio astronomy, signals from radio telescopes are transformed into images
of observed celestial objects, or sources. However, these images, called dirty
images, contain real sources as well as artifacts due to signal sparsity and
other factors. Therefore, radio interferometric image reconstruction is
performed on dirty images, aiming to produce clean images in which artifacts
are reduced and real sources are recovered. So far, existing methods have
limited success on recovering faint sources, preserving detailed structures,
and eliminating artifacts. In this paper, we present VIC-DDPM, a Visibility and
Image Conditioned Denoising Diffusion Probabilistic Model. Our main idea is to
use both the original visibility data in the spectral domain and dirty images
in the spatial domain to guide the image generation process with DDPM. This
way, we can leverage DDPM to generate fine details and eliminate noise, while
utilizing visibility data to separate signals from noise and retaining spatial
information in dirty images. We have conducted experiments in comparison with
both traditional methods and recent deep learning based approaches. Our results
show that our method significantly improves the resulting images by reducing
artifacts, preserving fine details, and recovering dim sources. This
advancement further facilitates radio astronomical data analysis tasks on
celestial phenomena.
