  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 instrument's 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.
