Accelerating the CLEAN algorithm of radio interferometry with convex optimization

TL;DR

The paper addresses the computational bottleneck in radio interferometric imaging by accelerating the major loop of CLEAN using convex-optimization techniques. By reframing CLEAN as an optimization problem, it shows that implicit gradient descent, conjugate gradient, and momentum methods can be mapped into CLEAN’s major/minor loop structure, producing significantly faster convergence than classical CLEAN. CG-CLEAN, in particular, reduces the number of major iterations by factors of several while achieving equal or superior dynamic range, and its performance is further enhanced when combined with advanced minor-loop deconvolution like Asp-CLEAN. Validation across CASA tutorials, synthetic ground-truth-like data, real VLA observations, and challenging VLBI/wideband regimes demonstrates robust speedups and reconstruction quality, suggesting a practical path to scalable imaging for next-generation radio arrays.

Abstract

In radio-interferometry, we recover an image from an incompletely sampled Fourier data. The de-facto standard algorithm, the Cotton-Schwab CLEAN, is iteratively switching between computing a deconvolution (minor loop) and subtracting the model from the visibilities (major loop). The next generation of radio interferometers is expected to deal with much higher data rates, image sizes and sensitivity, making an acceleration of current data processing algorithms necessary. We aim to achieve this by evaluating the potential of various well-known acceleration techniques in convex optimization to the major loop. For the present manuscript, we limit the scope to study these techniques only in the CLEAN framework. To this end, we identify CLEAN with a Newton scheme, and use this chain of arguments backwards to express Nesterov acceleration and conjugate gradient orthogonalization in the major and minor loop framework. The resulting algorithms are simple extensions of the traditional framework, but converge multiple times faster than traditional techniques, and reduce the residual significantly deeper. These improvements achieved by accelerating the major loop are competitive to well-known improvements by replacing the minor loop with more advanced algorithms, but at lower numerical cost. The best performance is achieved by combining these two developments.CLEAN remains among the fastest and most robust algorithms for imaging in radio interferometry, and can be easily extended to an almost an order of magnitude faster convergence speed and dynamic range. The procedure outlined in this manuscript is relatively straightforward and could be easily extended.

Figures (25)

• Figure 1: RMS as a function of major loop iteration for M31 obtained with Momentum-CLEAN with different values for $\mu$.
• Figure 2: Residual as a function of increasing major loop iterations (from left to right) for 3C391 for CLEAN (top row), Momentum CLEAN (middle row) and CG-CLEAN (bottom row).
• Figure 3: The recovered image of 3C391 with MS-CLEAN (left panel), Momentum-CLEAN (middle panel) and CG-CLEAN (right panel).
• Figure 4: Difference between current model and final model (after the last major loop iteration) as a function of increasing major loop iterations (from left to right) for 3C391 for CLEAN (top row), Momentum CLEAN (middle row) and CG-CLEAN (bottom row).
• Figure 5: Residual as a function of increasing major loop iterations (from left to right) for synthetic Cygnus A data for CLEAN (top row), Momentum CLEAN (middle row) and CG-CLEAN (bottom row).