Parallel faceted imaging in radio interferometry via proximal splitting (Faceted HyperSARA): I. Algorithm and simulations

Abstract

Upcoming radio interferometers are aiming to image the sky at new levels of resolution and sensitivity, with wide-band image cubes reaching close to the Petabyte scale for SKA. Modern proximal optimization algorithms have shown a potential to significantly outperform CLEAN thanks to their ability to inject complex image models to regularize the inverse problem for image formation from visibility data. They were also shown to be parallelizable over large data volumes thanks to a splitting functionality enabling the decomposition of the data into blocks, for parallel processing of block-specific data-fidelity terms involved in the objective function. Focusing on intensity imaging, the splitting functionality is further exploited in this work to decompose the image cube into spatio-spectral facets, and enable parallel processing of facet-specific regularization terms in the objective function, leading to the “Faceted HyperSARA” algorithm. Reliable heuristics enabling an automatic setting of the regularization parameters involved in the objective are also introduced, based on estimates of the noise level, transferred from the visibility domain to the domains where the regularization is applied. Simulation results based on a MATLAB implementation and involving synthetic image cubes and data close to Gigabyte size confirm that faceting can provide a major increase in parallelization capability when compared to the non-faceted approach (HyperSARA).

CLEANing Cygnus A Deep and Fast with R2D2

“…Further developments toward improving its capability to deliver new regimes of precision are warranted, e.g., by leveraging novel DNN architectures (including diffusion models; Ho et al 2020) and training loss functions for more efficient and physics-informed training and reconstruction. Finally, endowing the R2D2 paradigm with an image-splitting procedure, as implemented in DDFacet (Tasse et al 2018), WSClean (Offringa & Smirnov 2017), and Faceted HyperSARA (Thouvenin et al 2023), is a necessary evolution to efficiently handle large image sizes. In a nutshell, not only has CLEAN been leading the way for decades, but its algorithmic structure might well form the backbone of the next-generation deep learned-based imaging algorithms for radio astronomy.…”

Scalable precision wide-field imaging in radio interferometry: I. uSARA validated on ASKAP data

“…Nonetheless, our spectral analysis of the target sources remains preliminary and warrants a deeper study using wide-band imaging. Planned upgrades to the uSARA framework -which will incorporate joint DDE calibration ) and wide-band deconvolution (Thouvenin et al 2022a) -guarantee the robustness of future images, and consequently, more precise spectral information across all frequency channels.…”

“…𝑗 denotes the 𝑗 th coefficient of its argument vector, and (•) † stands for the adjoint of its argument operator. The parameter 𝜌 > 0 prevents the argument of the logarithmic from reaching zero values and can be set to the estimate of the noise level in the sparsity domain (Thouvenin et al 2022a)…”

“…Such innovative approaches -relying on sophisticated sparsity-based image models -have demonstrated their success at capturing both compact and diffuse components in the reconstructed radio images, albeit with an increase in computational expense. One such stateof-the-art optimisation-based class of methods is the "Sparsity Averaging Reweighted Analysis" (SARA) family (Carrillo et al 2012;Dabbech et al 2018;Abdulaziz et al 2019;Thouvenin et al 2022a, see the Puri-Psi web-page for more details). The monochromatic SARA algorithm, initially proposed by Carrillo et al (2012), leverages state-of-the-art algorithmic structures from optimisation theory to enforce non-negativity and sparsity in a highly redundant sparsity dictionary of the sought radio image under noise-driven data fidelity constraints (Onose et al 2016;Onose et al 2017).…”

Imaging algorithm of synthetic aperture radio telescope based on improved SARA

“…为了加快 SARA 的重构速度并提高其可扩展性, 研究 人员提出了几种快速的并行化算法, 如同时同向乘子 法 (Simultaneous-Direction Method of Multipliers, SDMM) [14] 、 交 替 方 向 乘 子 法 (Alternating Direction Method of Multipliers, ADMM) [15] 、前后向迭代原始对 偶 算 法 (Primal-Dual algorithm with Forward-Backward iterations, PDFB) [15] 和 预 处 理 原 始 对 偶 算 法 (Preconditioned Primal-Dual algorithm, PPD) [16] . 此 后 , SARA 算 法 扩 展 到 射 电 干 涉 极 化 成 像 (Polarized SARA) [17] 和宽带成像(HyperSARA) [18] [19] . 近年来, 研 究人员开始使用深度神经网络(deep neural networks, DNN)来进行端到端重构 [20][21] .…”