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Faraday tomography through broadband polarimetry can provide crucialinformation on magnetized astronomical objects, such as quasars, galaxies, orgalaxy clusters. However, the limited wavelength coverage of the instrumentsrequires that we solve an ill-posed inverse problem when we want to obtain theFaraday dispersion function (FDF), a tomographic distribution of themagnetoionic media along the line of sight. This paper explores the use ofwavelet transforms and the sparsity of the transformed FDFs in the form ofwavelet shrinkage (WS) for finding better solutions to the inverse problem. Werecently proposed the Constraining and Restoring iterative Algorithm forFaraday Tomography (CRAFT; Cooray et al. 2021), a new flexible algorithm thatshowed significant improvements over the popular methods such as RotationMeasure Synthesis. In this work, we introduce CRAFT+WS, a new version of CRAFTincorporating the ideas of wavelets and sparsity. CRAFT+WS exhibit significantimprovements over the original CRAFT when tested for a complex FDF of realisticGalactic model. Reconstructions of FDFs demonstrate super-resolution in Faradaydepth, uncovering previously unseen Faraday complexities in observations. Theproposed approach will be necessary for effective cosmic magnetism studiesusing the Square Kilometre Array and its precursors.

Wavelets and sparsity for Faraday tomography