[Paper Review] A practical preconditioner for wide-field continuum imaging of radio interferometric data

Hertzog L. Bester, Audrey Repetti+3 more|arXiv (Cornell University)|Jan 20, 2021

Soil Moisture and Remote Sensing4 citations

TL;DR

This paper proposes pfb-clean, a preconditioned forward-backward proximal algorithm that accelerates wide-field radio interferometric imaging by approximating the Hessian of the data fidelity term as convolution with the point spread function. The method reduces gradient evaluations to just 8, enabling fast, high-dynamic-range imaging with improved robustness to calibration artifacts compared to traditional CLEAN.

ABSTRACT

The celebrated CLEAN algorithm has been the cornerstone of deconvolution algorithms in radio interferometry almost since its conception in the 1970s. For all its faults, CLEAN is remarkably fast, robust to calibration artefacts and in its ability to model point sources. We demonstrate how the same assumptions that afford CLEAN its speed can be used to accelerate more sophisticated deconvolution algorithms.

Motivation & Objective

• To address the high computational cost of advanced deconvolution algorithms in wide-field radio interferometry, which limits their adoption despite superior performance.
• To develop a practical preconditioner that enables fast convergence in proximal gradient methods for imaging large-scale interferometric data.
• To reduce the number of expensive full measurement operator applications required by modern imaging algorithms.
• To maintain image quality and robustness while significantly lowering computational complexity for wide-field continuum imaging.

Proposed method

• The method approximates the Hessian of the data fidelity term as a convolution with the instrument's point spread function (PSF), enabling efficient preconditioning.
• It uses a preconditioner U = I^psf ⋆ + σId, where σ regularizes inversion and enables efficient conjugate gradient solves.
• The algorithm employs a preconditioned forward-backward proximal scheme with large step sizes (γ ≲ 1), minimizing exact gradient evaluations.
• It leverages dask-based implementations of wgridder and dask-ms for scalable, distributed measurement operator evaluation.
• The proximal step uses the primal-dual algorithm of Condat (2013) to handle non-smooth regularizers like the l2,1 norm.
• A positivity constraint is enforced via an indicator function in the regularizer, ensuring physically meaningful image reconstruction.

Experimental results

Research questions

• RQ1 Can a PSF-based Hessian approximation effectively precondition proximal gradient algorithms in wide-field radio imaging?
• RQ2 To what extent can this preconditioner reduce the number of full measurement operator applications in imaging algorithms?
• RQ3 How does the performance of the preconditioned algorithm compare to multi-scale CLEAN in terms of image quality and residual dynamics?
• RQ4 Can the method maintain robustness to calibration artifacts while achieving faster convergence?

Key findings

• pfb-clean achieved comparable image quality to wsclean's multi-scale CLEAN using only 8 gradient evaluations, significantly fewer than typical for advanced algorithms.
• The method produced naturally weighted residuals that respect flux positivity, unlike ms-clean, which can generate negative residuals.
• Despite higher per-iteration cost, pfb-clean's use of image-sized FFTs and wavelet transforms allows efficient parallelization and scalability.
• The algorithm demonstrated improved robustness to calibration artifacts when combined with a more expressive wavelet-based regularizer (Ψ), though sensitivity to artifacts increased with stronger regularization.
• The use of a preconditioner enabled large step sizes (γ ≲ 1), drastically reducing the number of full gradient evaluations required for convergence.