Faraday Tomography with Sparse Modeling

Faraday tomography (or rotation measure synthesis) is a procedure to convert linear polarization spectra into the Faraday dispersion function, which provides us with unique information of magneto-ionic media along the line of sight. Mathematical formulation of Faraday tomography is similar to polarimetric imaging of radio interferometry, where many new methods have been actively developed and shown to outperform the standard CLEAN approaches. In this paper, we propose a sparse reconstruction technique to Faraday tomography. This technique is being developed for interferometric imaging and utilizes computationally less expensive convex regularization functions such as $\ell_1$-norm and total variation (TV) or total squared variation (TSV). The proposed technique solves a convex optimization, and therefore its solution is determined uniquely regardless of the initial condition for given regularization parameters that can be optimized by data themselves. Using a physically-motivated model of turbulent galactic magnetized plasma, we demonstrate that the proposed technique outperforms RM-CLEAN and provides higher-fidelity reconstruction. The proposed technique would be a powerful tool in broadband polarimetry with the Square Kilometre Array (SKA) and its precursors.