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Diffusion models for polarimetric reconstruction of circumstellar environments

Quentin Villegas, Laurence Denneulin, Simon Prunet, André Ferrari, Nelly Pustelnik, Éric Thiébaut, Julian Tachella, Maud Langlois

TL;DR

This work tackles reconstructing circumstellar disk images from high-contrast polarimetric data where stellar leakage and missing data hinder inversion. It replaces the Rhapsodie prior with diffusion priors learned from synthetic data and uses Score-ALD to sample from the posterior $p(x|y,\lambda)$, with $x=(I_{\text{disk}}, I^{p})$ and $\lambda$ representing stellar leakage. The method computes the conditional score via $\nabla_{x_t}\log p(x_t|y,\lambda) \approx \nabla_{x_t}\log p(x_t) - \boldsymbol{\textsf{A}}^{\dagger}\boldsymbol{\textsf{W}}(\mathbf{I} + \gamma_t^2 \boldsymbol{\textsf{W}})^{-1}(\boldsymbol{\textsf{A}} x_t + \lambda \boldsymbol{\textsf{B}} s - y)$ and updates $\lambda$ with $\lambda_{t-1} = \dfrac{s^{\top} \boldsymbol{\textsf{B}}^{\top} \boldsymbol{\textsf{W}}(y - \boldsymbol{\textsf{A}} x_{t-1})}{\|\boldsymbol{\textsf{B}} s\|^2_{\boldsymbol{\textsf{W}}}}$ within an annealed Langevin scheme. On synthetic data from DDIt, the approach yields PSNR improvements of about $14$ dB over the Rhapsodie baseline and reduces MAE/RMSE by substantial factors, demonstrating better recovery of fine disk structure under high-contrast conditions. The results motivate future work in physics-informed diffusion and latent-diffusion variants to better handle more realistic leakage and observational conditions.

Abstract

In this paper, we propose an approach combining diffusion models and inverse problems for the reconstruction of circumstellar disk images. Our method builds upon the Rhapsodie framework for polarimetric imaging, substituting its classical prior with a diffusion model trained on synthetic data. Our formulation explicitly incorporates stellar leakage while efficiently handling missing data and high level noise inherent to high-contrast polarimetric imaging. Experiments show significant improvement over conventional methods within our framework of assumptions, opening new perspectives for studying circumstellar environments.

Diffusion models for polarimetric reconstruction of circumstellar environments

TL;DR

This work tackles reconstructing circumstellar disk images from high-contrast polarimetric data where stellar leakage and missing data hinder inversion. It replaces the Rhapsodie prior with diffusion priors learned from synthetic data and uses Score-ALD to sample from the posterior , with and representing stellar leakage. The method computes the conditional score via and updates with within an annealed Langevin scheme. On synthetic data from DDIt, the approach yields PSNR improvements of about dB over the Rhapsodie baseline and reduces MAE/RMSE by substantial factors, demonstrating better recovery of fine disk structure under high-contrast conditions. The results motivate future work in physics-informed diffusion and latent-diffusion variants to better handle more realistic leakage and observational conditions.

Abstract

In this paper, we propose an approach combining diffusion models and inverse problems for the reconstruction of circumstellar disk images. Our method builds upon the Rhapsodie framework for polarimetric imaging, substituting its classical prior with a diffusion model trained on synthetic data. Our formulation explicitly incorporates stellar leakage while efficiently handling missing data and high level noise inherent to high-contrast polarimetric imaging. Experiments show significant improvement over conventional methods within our framework of assumptions, opening new perspectives for studying circumstellar environments.
Paper Structure (12 sections, 14 equations, 1 figure, 1 table, 1 algorithm)

This paper contains 12 sections, 14 equations, 1 figure, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Formalisation du problème
  3. Modèle d'observation en polarimétrie
  4. Formulation du problème inverse
  5. Algorithme de reconstruction
  6. Processus de diffusion
  7. Méthode proposée pour la reconstruction
  8. Expériences et résultats
  9. Jeux de données et entraînement
  10. Évaluation des performances
  11. Conclusions et perspectives
  12. Remerciements :

Figures (1)

  • Figure 1: Ligne 1 : $I^p$, $I_{\text{disk}}$ et $I_{\text{disk}}+I_{\text{star}}$. Ligne 2 : reconstruction $I^p$, $I_{\text{disk}}$ et une des 4 mesures \ref{['eq:y_data_acquisition']} (ici $y_{0,0}$).