# A Conditional Denoising Diffusion Probabilistic Model for Radio Interferometric Image Reconstruction

arXiv: https://arxiv.org/abs/2305.09121 · HTML: https://mlsanity.com/paper/2305.09121/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 16 May 2023.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstruction](https://mlsanity.com/paper/2203.03623/) (2022)
- [Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging](https://mlsanity.com/paper/2010.14462/) (2020)

## Built on by (most cited first, 6 of 6)

- [FUSE: Fast Unified Simulation and Estimation for PDEs](https://mlsanity.com/paper/2405.14558/) (2024)
- [Radio-astronomical Image Reconstruction with Conditional Denoising Diffusion Model](https://mlsanity.com/paper/2402.10204/) (2024)
- [RADiff: Controllable Diffusion Models for Radio Astronomical Maps Generation](https://mlsanity.com/paper/2307.02392/) (2023)
- [PolarRec: Radio Interferometric Data Reconstruction with Polar Coordinate Representation](https://mlsanity.com/paper/2308.14610/) (2023)
- [VisRec: A Semi-Supervised Approach to Radio Interferometric Data Reconstruction](https://mlsanity.com/paper/2403.00897/) (2024)
- [VVTRec: Radio Interferometric Reconstruction through Visual and Textual Modality Enrichment](https://mlsanity.com/paper/2601.06475/) (2026)

## Abstract (arXiv)

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.