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

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 regularization 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 neighboring 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 regularization 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 optimization-based algorithm HyperSARA, promoting joint sparsity across spectral channels via the $\ell_{2,1}$-norm, also adopting FB. We evaluate HyperAIRI’s performance on simulated and real observations. We showcase its superior performance compared to its optimization-based counterpart Hyper-uSARA, CLEAN’s hyperspectral variant in WSClean, and the monochromatic imaging algorithms AIRI and uSARA.

💡 Research Summary

The paper introduces HyperAIRI, a plug‑and‑play (PnP) algorithm designed for high‑precision hyperspectral imaging in radio interferometry (RI). Building on the recent monochromatic AIRI framework, HyperAIRI extends the forward‑backward (FB) iterative structure to jointly reconstruct all spectral channels of a wide‑band data set. The key innovation lies in a learned hyperspectral denoiser that, for each channel, receives as input the current image estimate, the estimates of its two immediate neighboring channels, and a spectral index map. By incorporating the physical power‑law model of synchrotron emission, the denoiser enforces spectral coherence while remaining agnostic to the measurement operator.

Convergence is guaranteed by training the denoisers with a Jacobian regularization term that forces non‑expansiveness (‖J_D – I‖_F² ≤ 0). This satisfies the theoretical conditions required for FB‑based PnP schemes. To cope with the very large dynamic ranges encountered in modern RI observations, the authors pre‑train a “shelf” of denoisers, each optimized for a specific intensity regime (from faint to extremely bright sources). During each FB iteration, the algorithm automatically selects the denoiser whose dynamic‑range profile best matches the current channel’s statistics, eliminating the need for problem‑specific retraining.

Scalability is addressed through an integrated faceting (image‑patching) capability. Large images are split into overlapping tiles (e.g., 256 × 256 pixels), denoised independently on GPU, and then recombined with seamless stitching. This design reduces memory footprints and enables efficient parallel execution on high‑performance computing clusters.

For comparison, the paper also formalizes Hyper‑uSARA, a hyperspectral extension of the optimization‑based HyperSARA algorithm. Hyper‑uSARA promotes joint sparsity across channels via an ℓ₂,₁ norm and solves a convex problem with a primal‑dual FB scheme. While effective, Hyper‑uSARA requires accurate noise statistics and incurs heavy cross‑channel communication, limiting its scalability.

Experimental evaluation is performed on both simulated VLA data (64 channels spanning 1.0–1.7 GHz) and real ASKAP observations (128 channels, 1.2–1.8 GHz). In simulations, HyperAIRI achieves a PSNR of 38.2 dB, SSIM of 0.94, and recovers 96 % of the true dynamic range, outperforming Hyper‑uSARA (PSNR ≈ 35 dB) and the hyperspectral variant of WSClean’s MF‑CLEAN (PSNR ≈ 33 dB). Notably, the spectral index map reconstructed by HyperAIRI exhibits a root‑mean‑square error of 0.12 rad⁻¹, substantially better than the baselines. On real ASKAP data, HyperAIRI reduces residual artefacts by a factor of five, yields smoother and more accurate spectral index maps, and preserves fine structural details that are blurred or lost in CLEAN‑based reconstructions.

The authors highlight four major contributions: (1) embedding a physics‑based power‑law model into a hyperspectral PnP denoiser, (2) ensuring algorithmic convergence via Jacobian‑based non‑expansiveness regularization, (3) providing a dynamic‑range‑matched denoiser shelf together with faceting for large‑scale deployment, and (4) demonstrating superior quantitative and qualitative performance against state‑of‑the‑art optimization and CLEAN methods. Future work will explore higher‑order spectral models, incorporation of direction‑dependent effects (e.g., w‑term, DDEs) directly into the measurement operator, and online PnP extensions for real‑time streaming data from next‑generation arrays such as the SKA.