Faraday tomography offers crucial information on the magnetized astronomical objects, such as quasars, galaxies, or galaxy clusters, by observing its magnetoionic media. The observed linear polarization spectrum is inverse Fourier transformed to obtain the Faraday dispersion function (FDF), providing us a tomographic distribution of the magnetoionic media along the line of sight. However, this transform gives a poor reconstruction of the FDF because of the instruments limited wavelength coverage. The current Faraday tomography techniques inability to reliably solve the above inverse problem has noticeably plagued cosmic magnetism studies. We propose a new algorithm inspired by the well-studied area of signal restoration, called the Constraining and Restoring iterative Algorithm for Faraday Tomography (CRAFT). This iterative model-independent algorithm is computationally inexpensive and only requires weak physically-motivated assumptions to produce high fidelity FDF reconstructions. We demonstrate an application for a realistic synthetic model FDF of the Milky Way, where CRAFT shows greater potential over other popular model-independent techniques. The dependence of observational frequency coverage on the various techniques reconstruction performance is also demonstrated for a simpler FDF. CRAFT exhibits improvements even over model-dependent techniques (i.e., QU-fitting) by capturing complex multi-scale features of the FDF amplitude and polarization angle variations within a source. The proposed approach will be of utmost importance for future cosmic magnetism studies, especially with broadband polarization data from the Square Kilometre Array and its precursors. We make the CRAFT code publicly available.
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