# CosmoVAE: Variational Autoencoder for CMB Image Inpainting

arXiv: https://arxiv.org/abs/2001.11651 · HTML: https://mlsanity.com/paper/2001.11651/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2020.

## Built on by (most cited first, 4 of 4)

- [Approximate Equivariance SO(3) Needlet Convolution](https://mlsanity.com/paper/2206.10385/) (2022)
- [A Comprehensive Review of Diffusion Models in Smart Agriculture: Progress, Applications, and Challenges](https://mlsanity.com/paper/2507.18376/) (2025)
- [An Analysis of Generative Methods for Multiple Image Inpainting](https://mlsanity.com/paper/2205.02146/) (2022)
- [Modelling nonlinear dependencies in the latent space of inverse scattering](https://mlsanity.com/paper/2203.10307/) (2022)

## Abstract (arXiv)

Cosmic microwave background radiation (CMB) is critical to the understanding of the early universe and precise estimation of cosmological constants. Due to the contamination of thermal dust noise in the galaxy, the CMB map that is an image on the two-dimensional sphere has missing observations, mainly concentrated on the equatorial region. The noise of the CMB map has a significant impact on the estimation precision for cosmological parameters. Inpainting the CMB map can effectively reduce the uncertainty of parametric estimation. In this paper, we propose a deep learning-based variational autoencoder --- CosmoVAE, to restoring the missing observations of the CMB map. The input and output of CosmoVAE are square images. To generate training, validation, and test data sets, we segment the full-sky CMB map into many small images by Cartesian projection. CosmoVAE assigns physical quantities to the parameters of the VAE network by using the angular power spectrum of the Gaussian random field as latent variables. CosmoVAE adopts a new loss function to improve the learning performance of the model, which consists of ℓ1 reconstruction loss, Kullback-Leibler divergence between the posterior distribution of encoder network and the prior distribution of latent variables, perceptual loss, and total-variation regularizer. The proposed model achieves state of the art performance for Planck textttCommander 2018 CMB map inpainting.