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HyperAIRI: a plug-and-play algorithm for precise hyperspectral image reconstruction in radio interferometry

Chao Tang, Arwa Dabbech, Adrian Jackson, Yves Wiaux

TL;DR

HyperAIRI extends AIRI to hyperspectral RI imaging by using learned, non-expansive denoisers that operate on nearby spectral channels and incorporate a power-law spectral model via a spectral correction layer. The approach is complemented by Hyper-uSARA, an unconstrained optimization-based variant, enabling robust joint-channel reconstruction with scalable, parallel computation. Across simulated VLA data and real ASKAP observations, HyperAIRI delivers higher SNR, improved logSNR for faint emissions, better spectral coherence, and competitive data fidelity compared with Hyper-uSARA, AIRI, uSARA, and WSClean. The method achieves strong precision and scalability through channel-wise parallelism and spatial facet processing, positioning it as a practical tool for next-generation wideband RI imaging.

Abstract

The next-generation radio-interferometric (RI) telescopes require imaging algorithms capable of forming high-resolution high-dynamic-range images from large data volumes spanning wide frequency bands. Recently, AIRI, a plug-and-play (PnP) approach taking the forward-backward algorithmic structure (FB), has demonstrated state-of-the-art performance in monochromatic RI imaging by alternating a data-fidelity step with a regularisation step via learned denoisers. In this work, we introduce HyperAIRI, its hyperspectral extension, underpinned by learned hyperspectral denoisers enforcing a power-law spectral model. For each spectral channel, the HyperAIRI denoiser takes as input its current image estimate, alongside estimates of its two immediate neighbouring channels and the spectral index map, and provides as output its associated denoised image. To ensure convergence of HyperAIRI, the denoisers are trained with a Jacobian regularisation enforcing non-expansiveness. To accommodate varying dynamic ranges, we assemble a shelf of pre-trained denoisers, each tailored to a specific dynamic range. At each HyperAIRI iteration, the spectral channels of the target image cube are updated in parallel using dynamic-range-matched denoisers from the pre-trained shelf. The denoisers are also endowed with a spatial image faceting functionality, enabling scalability to varied image sizes. Additionally, we formally introduce Hyper-uSARA, a variant of the optimisation-based algorithm HyperSARA, promoting joint sparsity across spectral channels via the l2,1-norm, also adopting FB. We evaluate HyperAIRI's performance on simulated and real observations. We showcase its superior performance compared to its optimisation-based counterpart Hyper-uSARA, CLEAN's hyperspectral variant in WSClean, and the monochromatic imaging algorithms AIRI and uSARA.

HyperAIRI: a plug-and-play algorithm for precise hyperspectral image reconstruction in radio interferometry

TL;DR

HyperAIRI extends AIRI to hyperspectral RI imaging by using learned, non-expansive denoisers that operate on nearby spectral channels and incorporate a power-law spectral model via a spectral correction layer. The approach is complemented by Hyper-uSARA, an unconstrained optimization-based variant, enabling robust joint-channel reconstruction with scalable, parallel computation. Across simulated VLA data and real ASKAP observations, HyperAIRI delivers higher SNR, improved logSNR for faint emissions, better spectral coherence, and competitive data fidelity compared with Hyper-uSARA, AIRI, uSARA, and WSClean. The method achieves strong precision and scalability through channel-wise parallelism and spatial facet processing, positioning it as a practical tool for next-generation wideband RI imaging.

Abstract

The next-generation radio-interferometric (RI) telescopes require imaging algorithms capable of forming high-resolution high-dynamic-range images from large data volumes spanning wide frequency bands. Recently, AIRI, a plug-and-play (PnP) approach taking the forward-backward algorithmic structure (FB), has demonstrated state-of-the-art performance in monochromatic RI imaging by alternating a data-fidelity step with a regularisation step via learned denoisers. In this work, we introduce HyperAIRI, its hyperspectral extension, underpinned by learned hyperspectral denoisers enforcing a power-law spectral model. For each spectral channel, the HyperAIRI denoiser takes as input its current image estimate, alongside estimates of its two immediate neighbouring channels and the spectral index map, and provides as output its associated denoised image. To ensure convergence of HyperAIRI, the denoisers are trained with a Jacobian regularisation enforcing non-expansiveness. To accommodate varying dynamic ranges, we assemble a shelf of pre-trained denoisers, each tailored to a specific dynamic range. At each HyperAIRI iteration, the spectral channels of the target image cube are updated in parallel using dynamic-range-matched denoisers from the pre-trained shelf. The denoisers are also endowed with a spatial image faceting functionality, enabling scalability to varied image sizes. Additionally, we formally introduce Hyper-uSARA, a variant of the optimisation-based algorithm HyperSARA, promoting joint sparsity across spectral channels via the l2,1-norm, also adopting FB. We evaluate HyperAIRI's performance on simulated and real observations. We showcase its superior performance compared to its optimisation-based counterpart Hyper-uSARA, CLEAN's hyperspectral variant in WSClean, and the monochromatic imaging algorithms AIRI and uSARA.
Paper Structure (28 sections, 29 equations, 10 figures, 2 tables, 2 algorithms)

This paper contains 28 sections, 29 equations, 10 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Hyperspectral RI imaging
  3. Hyperspectral radio emission model
  4. Hyperspectral Fourier sampling in RI
  5. RI hyperspectral inverse problem
  6. Optimisation-based hyperspectral imaging
  7. Optimisation theory
  8. Hyperspectral SARA prior and Hyper-uSARA
  9. HyperAIRI
  10. Hyperspectral PnP-FB and HyperAIRI denoiser
  11. Training HyperAIRI denoisers
  12. Algorithmic structure
  13. Initialisation
  14. Reconstruction loop
  15. Dynamic denoiser and spectral index map update
  16. ...and 13 more sections

Figures (10)

  • Figure 1: A set of simulated VLA hyperspectral sampling patterns of different channels. The three panels show the normalised $uv$ sampling patterns for the first, middle and last channels of an observation with frequencies 1.00, 1.34 and 1.70 GHz, respectively. The coordinates are in the unit of wavelength.
  • Figure 2: HyperAIRI algorithm structure. Panels illustrate the following: (a) HyperAIRI denoiser architecture; (b) the inner structure of the spectral correction layer; (c) the flowchart of HyperAIRI algorithm; and (d) HyperAIRI's FB iteration structure.
  • Figure 3: Original ground-truth images for generating the simulated test dataset. Each image has a size of $512 \times 512$ and the names of the sources are listed below the images.
  • Figure 4: Channel-wise reconstruction metrics for various methods on the simulated test set. The channel index ranges from 1 to 36. From top to bottom, the panels show SNR, logSNR and RDR versus channel index, respectively. Each point represents the average metrics value for the corresponding channel index across all problems, and the shaded areas indicate the $95\%$ confidence interval.
  • Figure 5: Reconstruction results of a simulated inverse problem using radio galaxy image of 3C 353. Row 1 shows the ground truth. Row 2-6 show results from uSARA, AIRI, WSClean, Hyper-uSARA, and HyperAIRI. Columns 1 and 3 display estimated images at the first and last channels in a logarithmic scale. Columns 2 and 4 display the back-projected dirty images (row 1, normalized to $[0,1]$) or the back-projected residual images (rows 2-6). column 5 illustrates the spectral index maps. Two zoomed-in regions, one focusing on the central black hole and the other on a hotspot to the right, highlight visual differences. Channel-wise SNR and logSNR values (dB) are indicated at at the bottom-right corners of panels in columns 1 and 3, RDR values ($10^{-3}$) in columns 2 and 4 (with ground-truth values in row 1), and sSNR values (dB) in columns 5. Overall metrics for the entire image cube are listed next to each algorithm name, with units matching with the channel-wise metrics. The ground-truth overall RDR value is included in the top-left bracket of row 1.
  • ...and 5 more figures