Radio interferometric gain calibration as a complex optimization problem

Recent developments in optimization theory have extended some traditional algorithms for least-squares optimization of real-valued functions (Gauss–Newton, Levenberg–Marquardt, etc.) into the domain of complex functions of a complex variable. This employs a formalism called the Wirtinger derivative,...

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Bibliographic Details
Published in:Monthly notices of the Royal Astronomical Society Vol. 449; no. 3; pp. 2668 - 2684
Main Authors: Smirnov, O. M., Tasse, C.
Format: Journal Article
Language:English
Published: London Oxford University Press 21.05.2015
Oxford University Press (OUP): Policy P - Oxford Open Option A
Subjects:
Algorithms
Astronauts
Astronomy
Astrophysics
Calibration
Formalism
Gain
Interferometry
Jacobians
Mathematical analysis
Mathematical models
Optimization
Optimization algorithms
Sciences of the Universe
methods: analytical
methods: numerical
instrumentation: interferometers
techniques: interferometric
Astrophysics - Instrumentation and Methods for Astrophysics
ISSN:0035-8711, 1365-2966
Online Access:Get full text
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Summary:Recent developments in optimization theory have extended some traditional algorithms for least-squares optimization of real-valued functions (Gauss–Newton, Levenberg–Marquardt, etc.) into the domain of complex functions of a complex variable. This employs a formalism called the Wirtinger derivative, and derives a full-complex Jacobian counterpart to the conventional real Jacobian. We apply these developments to the problem of radio interferometric gain calibration, and show how the general complex Jacobian formalism, when combined with conventional optimization approaches, yields a whole new family of calibration algorithms, including those for the polarized and direction-dependent gain regime. We further extend the Wirtinger calculus to an operator-based matrix calculus for describing the polarized calibration regime. Using approximate matrix inversion results in computationally efficient implementations; we show that some recently proposed calibration algorithms such as StefCal and peeling can be understood as special cases of this, and place them in the context of the general formalism. Finally, we present an implementation and some applied results of CohJones, another specialized direction-dependent calibration algorithm derived from the formalism.
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ISSN:0035-8711
1365-2966
DOI:10.1093/mnras/stv418