Applying Wirtinger derivatives to the radio interferometry calibration problem

TL;DR

This paper introduces a fast, efficient calibration algorithm for radio interferometry using Wirtinger derivatives, leveraging sparsity in the Jacobian to improve computational performance.

Contribution

It applies Wirtinger derivatives to radio interferometry calibration, resulting in a computationally efficient algorithm with a sparse Jacobian structure.

Findings

Significant reduction in algorithmic cost due to Jacobian sparsity

Effective full-polarisation, direction-dependent calibration demonstrated

Potential for real-time radio interferometry calibration

Abstract

This paper presents a fast algorithm for full-polarisation, direction dependent calibration in radio interferometry. It is based on Wirtinger's approach to complex differentiation. Compared to the classical case, and under reasonable approximations, the Jacobian appearing in the Levenberg-Maquardt iterative scheme presents a sparse structure, allowing for high gain in terms of algorithmic cost.