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Uncertainty quantification for fast reconstruction methods using augmented equivariant bootstrap: Application to radio interferometry

Mostafa Cherif, Tobías I. Liaudat, Jonathan Kern, Christophe Kervazo, Jérôme Bobin

TL;DR

The paper tackles uncertainty quantification for fast radio-interferometric image reconstruction under incomplete uv-coverage, where forward-model null spaces drive large uncertainties. It introduces Conformalized Augmented Radio Bootstrap (CARB), a method that leverages an equivariant bootstrap over problem-tailored group actions and a conformalization step (RCPS) to produce calibrated, per-pixel uncertainty intervals around ultra-fast unrolled reconstructions. CARB uses diverse forward operators $\bar{M} T_{g}$, including translations, flips, rotations, and shelving filters, combined with an unrolled network (EVIL-Deconv) to achieve speed and accuracy, and demonstrates improved coverage over standard bootstrap and conformal QR on MeerKAT PSF-simulated RI data. The approach provides reliable, interpretable UQ for RI reconstructions relevant to next-generation instruments like the SKA, with practical runtimes and scalable computation.

Abstract

The advent of next-generation radio interferometers like the Square Kilometer Array promises to revolutionise our radio astronomy observational capabilities. The unprecedented volume of data these devices generate requires fast and accurate image reconstruction algorithms to solve the ill-posed radio interferometric imaging problem. Most state-of-the-art reconstruction methods lack trustworthy and scalable uncertainty quantification, which is critical for the rigorous scientific interpretation of radio observations. We propose an unsupervised technique based on a conformalized version of a radio-augmented equivariant bootstrapping method, which allows us to quantify uncertainties for fast reconstruction methods. Noticeably, we rely on reconstructions from ultra-fast unrolled algorithms. The proposed method brings more reliable uncertainty estimations to our problem than existing alternatives.

Uncertainty quantification for fast reconstruction methods using augmented equivariant bootstrap: Application to radio interferometry

TL;DR

The paper tackles uncertainty quantification for fast radio-interferometric image reconstruction under incomplete uv-coverage, where forward-model null spaces drive large uncertainties. It introduces Conformalized Augmented Radio Bootstrap (CARB), a method that leverages an equivariant bootstrap over problem-tailored group actions and a conformalization step (RCPS) to produce calibrated, per-pixel uncertainty intervals around ultra-fast unrolled reconstructions. CARB uses diverse forward operators , including translations, flips, rotations, and shelving filters, combined with an unrolled network (EVIL-Deconv) to achieve speed and accuracy, and demonstrates improved coverage over standard bootstrap and conformal QR on MeerKAT PSF-simulated RI data. The approach provides reliable, interpretable UQ for RI reconstructions relevant to next-generation instruments like the SKA, with practical runtimes and scalable computation.

Abstract

The advent of next-generation radio interferometers like the Square Kilometer Array promises to revolutionise our radio astronomy observational capabilities. The unprecedented volume of data these devices generate requires fast and accurate image reconstruction algorithms to solve the ill-posed radio interferometric imaging problem. Most state-of-the-art reconstruction methods lack trustworthy and scalable uncertainty quantification, which is critical for the rigorous scientific interpretation of radio observations. We propose an unsupervised technique based on a conformalized version of a radio-augmented equivariant bootstrapping method, which allows us to quantify uncertainties for fast reconstruction methods. Noticeably, we rely on reconstructions from ultra-fast unrolled algorithms. The proposed method brings more reliable uncertainty estimations to our problem than existing alternatives.

Paper Structure

This paper contains 14 sections, 10 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Radio-interferometric imaging problem
  3. Uncertainty Quantification Methods
  4. Conformalized Augmented Radio Bootstrap (CARB)
  5. Numerical experiments
  6. Data
  7. Results
  8. Radio-interferometry image reconstruction using an unrolled algorithm
  9. Unrolling method
  10. Unrolling results
  11. Point spread function and uv-coverage
  12. Conformalization
  13. Choice of the number of bootstrap samples
  14. Additional results

Figures (7)

  • Figure 1: 1D radial visualization of shelving filters.
  • Figure 2: RI image reconstruction result for the unrolling algorithm. From left to right, the figures correspond to: the ground truth observation; the simulated point spread function (PSF); the observed image after the application of the PSF and the observational noise; and the reconstructed image from EVIL-Deconv.
  • Figure 3: Pixel-wise uncertainty quantification represented by the $90$-th quantile estimation. Subfigure (\ref{['absres']}) shows the oracle absolute residuals. Then, the estimation of each method is presented: (\ref{['qr']}) quantile regression, (\ref{['cqr']}) conformalized quantile regression, (\ref{['pb']}) parametric bootstrap, (\ref{['eb']}) equivariant bootstrap, (\ref{['arb']}) augmented radio bootstrap and (\ref{['carb']}) conformalized augmented radio bootstrap.
  • Figure 4: Coverage plots for the equivariant bootstrap methods with different group actions.
  • Figure 5: Examples of the simulated MeerKAT PSFs and their associated uv-coverage.
  • ...and 2 more figures