Accelerating the CLEAN algorithm of radio interferometry with convex optimization

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.

💡 Research Summary

The paper addresses the pressing need to speed up radio‑interferometric imaging as next‑generation arrays such as the SKA, ngVLA, and DSA‑2000 will produce vastly larger data volumes. While the Cotton‑Schwab CLEAN algorithm remains the work‑horse because of its simplicity, robustness, and modular major/minor loop structure, it has never incorporated modern convex‑optimization acceleration techniques. The authors first recast CLEAN in the language of optimization: the major loop updates the image estimate by applying the adjoint measurement operator Φ⁺ to the visibility residual, which is exactly the gradient of the quadratic data‑fidelity functional J(θ)=½‖V−Φθ‖²_Y. Consequently, the major loop is a first‑order gradient descent step, and the whole CLEAN process can be viewed as a Newton‑type scheme where the minor loop supplies an approximate solution to the deconvolution sub‑problem.

Building on this interpretation, two well‑known acceleration strategies are transplanted into the major loop. (1) Nesterov momentum introduces a predictive extrapolation θ̃_k = θ_k + β_k(θ_k−θ_{k−1}) before computing the residual, with β_k following the classic schedule (t_k−1)/(t_k+2). This yields the theoretical O(1/k²) convergence rate of accelerated gradient methods. (2) Conjugate‑Gradient (CG) orthogonalization constructs a new search direction d_k = g_k + γ_k d_{k−1}, where g_k is the current gradient and γ_k is computed via Fletcher‑Reeves or Polak‑Ribiere formulas. CG ensures that successive directions are conjugate with respect to the (implicitly approximated) Hessian, improving convergence especially when the measurement operator Φ is ill‑conditioned due to non‑uniform weighting or direction‑dependent effects.

The authors implement these schemes as lightweight modifications to existing CLEAN pipelines (e.g., CASA, WSClean) without altering the minor loop. Experiments on synthetic data show that, for a target residual level of –30 dB, the Nesterov‑accelerated major loop reduces the number of major‑loop iterations by a factor of 4–5 on average, while the CG‑augmented version achieves similar gains with slightly better robustness to noise. The residual spectra are deeper, indicating an increase in dynamic range of roughly 1.5–2×.

Real‑world tests on VLA and ALMA observations confirm the synthetic results. Even in the presence of complex source morphology and direction‑dependent calibration terms, the accelerated major loops converge 3–6 times faster than the classic implementation, and the final images retain comparable peak signal‑to‑noise ratios and structural fidelity. When compared against advanced minor‑loop variants such as Multi‑Scale CLEAN or MS‑CLEAN, the accelerated major loop alone reaches comparable dynamic range while incurring only ~30 % additional computational cost.

Finally, the paper explores a hybrid configuration that combines the accelerated major loop with state‑of‑the‑art minor‑loop techniques (e.g., sparsity‑based regularization, deep‑learning preconditioners). This synergy yields almost an order‑of‑magnitude speed‑up for the full imaging pipeline, with memory footprints remaining within the limits of current hardware. The authors argue that such a hybrid approach is well‑suited for the massive data streams expected from upcoming interferometers, providing a path to near‑real‑time imaging without sacrificing the robustness and ease of use that have made CLEAN the de‑facto standard.

In conclusion, by interpreting CLEAN as a Newton‑type optimizer and injecting Nesterov and CG acceleration into its major loop, the authors achieve up to ten‑fold improvements in convergence speed and notable gains in dynamic range, all while preserving the algorithm’s simplicity and compatibility with existing software ecosystems. This work demonstrates that even legacy algorithms can benefit dramatically from modern convex‑optimization insights, opening the door to further enhancements when combined with advanced minor‑loop strategies.