The application of compressive sampling to radio astronomy II: Faraday rotation measure synthesis

TL;DR

This paper introduces three novel compressive sensing-based algorithms for Faraday rotation measure synthesis, significantly improving the reconstruction of magnetic field structures from limited radio polarization data.

Contribution

It presents new CS algorithms tailored for different source types in RM synthesis, enhancing reconstruction accuracy over traditional methods.

Findings

Superior reconstruction of magnitude and phase compared to RM-CLEAN

Effective for Faraday thin, thick, and mixed sources

Visual and numerical validation of improved performance

Abstract

Faraday rotation measure (RM) synthesis is an important tool to study and analyze galactic and extra-galactic magnetic fields. Since there is a Fourier relation between the Faraday dispersion function and the polarized radio emission, full reconstruction of the dispersion function requires knowledge of the polarized radio emission at both positive and negative square wavelengths $\lambda^2$. However, one can only make observations for $\lambda^2 > 0$. Furthermore observations are possible only for a limited range of wavelengths. Thus reconstructing the Faraday dispersion function from these limited measurements is ill-conditioned. In this paper, we propose three new reconstruction algorithms for RM synthesis based upon compressive sensing/sampling (CS). These algorithms are designed to be appropriate for Faraday thin sources only, thick sources only, and mixed sources respectively. Both visual and numerical results show that the new RM synthesis methods provide superior reconstructions of both magnitude and phase information than RM-CLEAN