Wavelets and sparsity for Faraday tomography
  Faraday tomography through broadband polarimetry can provide crucial
information on magnetized astronomical objects, such as quasars, galaxies, or
galaxy clusters. However, the limited wavelength coverage of the instruments
requires that we solve an ill-posed inverse problem when we want to obtain the
Faraday dispersion function (FDF), a tomographic distribution of the
magnetoionic media along the line of sight. This paper explores the use of
wavelet transforms and the sparsity of the transformed FDFs in the form of
wavelet shrinkage (WS) for finding better solutions to the inverse problem. We
recently proposed the Constraining and Restoring iterative Algorithm for
Faraday Tomography (CRAFT; Cooray et al. 2021), a new flexible algorithm that
showed significant improvements over the popular methods such as Rotation
Measure Synthesis. In this work, we introduce CRAFT+WS, a new version of CRAFT
incorporating the ideas of wavelets and sparsity. CRAFT+WS exhibit significant
improvements over the original CRAFT when tested for a complex FDF of realistic
Galactic model. Reconstructions of FDFs demonstrate super-resolution in Faraday
depth, uncovering previously unseen Faraday complexities in observations. The
proposed approach will be necessary for effective cosmic magnetism studies
using the Square Kilometre Array and its precursors.
