Adaptive ADMM in Distributed Radio Interferometric Calibration

TL;DR

This paper enhances distributed radio interferometric calibration by integrating adaptive penalty updates into ADMM, demonstrating improved convergence and stability over fixed penalty methods through simulations.

Contribution

It introduces adaptive penalty parameter updates into ADMM for radio interferometric calibration, comparing residual balance and spectral schemes for better performance.

Findings

Adaptive penalty updates improve ADMM convergence.

Spectral penalty update offers greater stability.

Both adaptive methods outperform fixed penalty ADMM.

Abstract

Distributed radio interferometric calibration based on consensus optimization has been shown to improve the estimation of systematic errors in radio astronomical observations. The intrinsic continuity of systematic errors across frequency is used by a consensus polynomial to penalize traditional calibration. Consensus is achieved via the use of alternating direction method of multipliers (ADMM) algorithm. In this paper, we extend the existing distributed calibration algorithms to use ADMM with an adaptive penalty parameter update. Compared to a fixed penalty, its adaptive update has been shown to perform better in diverse applications of ADMM. In this paper, we compare two such popular penalty parameter update schemes: residual balance penalty update and spectral penalty update (Barzilai-Borwein). We apply both schemes to distributed radio interferometric calibration and compare their performance against ADMM with a fixed penalty parameter. Simulations show that both methods of adaptive penalty update improve the convergence of ADMM but the spectral penalty parameter update shows more stability.