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R2D2 image reconstruction with model uncertainty quantification in radio astronomy

Amir Aghabiglou, Chung San Chu, Arwa Dabbech, Yves Wiaux

TL;DR

The paper tackles the ill-posed nature of radio-interferometric imaging by proposing R2D2, a residual-to-residual DNN series that iteratively refines images. By training multiple realizations and forming R2D2 samples, it provides joint image reconstruction and epistemic uncertainty maps, enabling robust, scalable high-dynamic-range RI imaging. Across simulations and real VLA data (Cygnus A), R2D2 outperforms CLEAN, U‑Net, uSARA, and AIRI in accuracy and speed, while exhibiting low model uncertainty that rapidly decreases with the number of terms in the series. This ensemble-based uncertainty quantification approach makes R2D2 particularly well-suited for large surveys, combining fast reconstruction with interpretable uncertainty information.

Abstract

The ``Residual-to-Residual DNN series for high-Dynamic range imaging'' (R2D2) approach was recently introduced for Radio-Interferometric (RI) imaging in astronomy. R2D2's reconstruction is formed as a series of residual images, iteratively estimated as outputs of Deep Neural Networks (DNNs) taking the previous iteration's image estimate and associated data residual as inputs. In this work, we investigate the robustness of the R2D2 image estimation process, by studying the uncertainty associated with its series of learned models. Adopting an ensemble averaging approach, multiple series can be trained, arising from different random DNN initializations of the training process at each iteration. The resulting multiple R2D2 instances can also be leveraged to generate ``R2D2 samples'', from which empirical mean and standard deviation endow the algorithm with a joint estimation and uncertainty quantification functionality. Focusing on RI imaging, and adopting a telescope-specific approach, multiple R2D2 instances were trained to encompass the most general observation setting of the Very Large Array (VLA). Simulations and real-data experiments confirm that: (i) R2D2's image estimation capability is superior to that of the state-of-the-art algorithms; (ii) its ultra-fast reconstruction capability (arising from series with only few DNNs) makes the computation of multiple reconstruction samples and of uncertainty maps practical even at large image dimension; (iii) it is characterized by a very low model uncertainty.

R2D2 image reconstruction with model uncertainty quantification in radio astronomy

TL;DR

The paper tackles the ill-posed nature of radio-interferometric imaging by proposing R2D2, a residual-to-residual DNN series that iteratively refines images. By training multiple realizations and forming R2D2 samples, it provides joint image reconstruction and epistemic uncertainty maps, enabling robust, scalable high-dynamic-range RI imaging. Across simulations and real VLA data (Cygnus A), R2D2 outperforms CLEAN, U‑Net, uSARA, and AIRI in accuracy and speed, while exhibiting low model uncertainty that rapidly decreases with the number of terms in the series. This ensemble-based uncertainty quantification approach makes R2D2 particularly well-suited for large surveys, combining fast reconstruction with interpretable uncertainty information.

Abstract

The ``Residual-to-Residual DNN series for high-Dynamic range imaging'' (R2D2) approach was recently introduced for Radio-Interferometric (RI) imaging in astronomy. R2D2's reconstruction is formed as a series of residual images, iteratively estimated as outputs of Deep Neural Networks (DNNs) taking the previous iteration's image estimate and associated data residual as inputs. In this work, we investigate the robustness of the R2D2 image estimation process, by studying the uncertainty associated with its series of learned models. Adopting an ensemble averaging approach, multiple series can be trained, arising from different random DNN initializations of the training process at each iteration. The resulting multiple R2D2 instances can also be leveraged to generate ``R2D2 samples'', from which empirical mean and standard deviation endow the algorithm with a joint estimation and uncertainty quantification functionality. Focusing on RI imaging, and adopting a telescope-specific approach, multiple R2D2 instances were trained to encompass the most general observation setting of the Very Large Array (VLA). Simulations and real-data experiments confirm that: (i) R2D2's image estimation capability is superior to that of the state-of-the-art algorithms; (ii) its ultra-fast reconstruction capability (arising from series with only few DNNs) makes the computation of multiple reconstruction samples and of uncertainty maps practical even at large image dimension; (iii) it is characterized by a very low model uncertainty.
Paper Structure (12 sections, 11 equations, 4 figures, 1 table)

This paper contains 12 sections, 11 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. R2D2 methodology
  3. Image Reconstruction
  4. Robustness & Uncertainty Quantification
  5. Validation
  6. Training Dataset and Training
  7. Simulations: Test Dataset
  8. Simulations: Benchmark algorithms
  9. Simulations: Metrics
  10. Simulations: Results & Discussion
  11. Real Data Proof of Concept
  12. Conclusion

Figures (4)

  • Figure 1: Evolution of the R2D2 series (single realization) across its iterations. The ground truth image $\boldsymbol{x}^{\star}$ and dirty image $\boldsymbol{r}^{(0)}_{\textrm{R2D2}}$ are reported in the top left and center panels, respectively. The output of the first DNN gives $\hat{\boldsymbol{x}}^{(1)}_{\textrm{R2D2}}$ (top right). 12 iterations later, $\boldsymbol{r}^{(11)}_{\textrm{R2D2}}$ (bottom left) and $\hat{\boldsymbol{x}}^{(12)}_{\textrm{R2D2}}$ are fed to the last DNN, whose output (bottom center) is added to $\hat{\boldsymbol{x}}^{(12)}_{\textrm{R2D2}}$ to deliver the reconstruction (bottom right).
  • Figure 2: Quantitative metric analysis. Left (resp. center): Progress of the reconstruction quality evaluated by SNR (resp. logSNR) across R2D2 iterations for both $\mu(\bar{\boldsymbol{x}}^{(i)})_{\textrm{R2D2}}$ and ${\hat{\boldsymbol{x}}^{(i)}}_{\textrm{R2D2}}$. Right: Progress of the epistemic uncertainty evaluated by $[\sigma/\mu](\bar{\boldsymbol{x}}^{(i)})_{\textrm{R2D2}}$ across iterations. Values of the SNR and logSNR, achieved at convergence by the benchmark algorithms uSARA and CLEAN, are reported via horizontal lines, in their respective plots. Each point is the averaged metric over 200 inverse problems (5$\times$200 for $\hat{\boldsymbol{x}}_{\textrm{R2D2}}$), while the shaded area presents its standard deviations.
  • Figure 3: Visual illustration of the R2D2 joint image estimation and uncertainty quantification functionality across iterations for the simulation results. Top row: ground truth (left) and dirty image (right). Second row: reconstruction $\hat{\boldsymbol{x}}_{\textrm{uSARA}}$ (left) and $\hat{\boldsymbol{x}}_{\textrm{CLEAN}}$ (right). Third (resp. fourth, fifth) row: $\mu(\bar{\boldsymbol{x}}^{(i)})_{\textrm{R2D2}}$ (left) and $[\sigma/\mu](\bar{\boldsymbol{x}}^{(i)})_{\textrm{R2D2}}$ (right) for iterations $i=1$ (U-Net) (resp. $i=3$, $i=12$). The evaluation metrics (SNR, logSNR) are embedded inside each image estimate. The mean pixel values across the image is shown inside each uncertainty image.
  • Figure 4: Visual illustration of the R2D2 joint image estimation and uncertainty quantification functionality across iterations for the real data results. Left: pixel-wise mean $\mu(\bar{\boldsymbol{x}}^{(12)})_{\textrm{R2D2}}$. Right: uncertainty map $[\sigma/\mu](\bar{\boldsymbol{x}}^{(12)})_{\textrm{R2D2}}$.