Sparse Faraday Rotation Measure Synthesis

Faraday rotation measure synthesis is a method for analyzing multichannel polarized radio emissions, and it has emerged as an important tool in the study of galactic and extra-galactic magnetic fields. The method requires the recovery of the Faraday dispersion function from measurements restricted to limited wavelength ranges, which is an ill-conditioned deconvolution problem. Here, we discuss a recovery method, which assumes a sparse approximation of the Faraday dispersion function in an over-complete dictionary of functions. We discuss the general case, when both thin and thick components are included in the model, and we present the implementation of a greedy deconvolution algorithm. We illustrate the method with several numerical simulations that emphasize the effect of the covered range and sampling resolution in the Faraday depth space, and the effect of noise on the observed data.