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.
