Reconstruction of Faraday Dispersion Function Based on Compressive Sensing Method

Faraday dispersion function (FDF) contains information on magnetic fields within the emitting sources and the medium between sources and observers. However, it is very challenging to properly reconstruct FDFs from observed data. Recently, the compressive sensing algorithm has been proposed to recover FDFs. Whether this method is practicable or not is yet to be explored. In this paper, we thoroughly aim at the application of compressive sensing algorithm. We make a large sample of simulations with parameters consistent with observations and apply the compressive sensing method to the data. We find that the reconstructed results are affected by various factors, such as the number of emitting components and the separation of these components in Faraday depth domain. We suggest that the peak of FDFs be located with parabolic fitting and the resolution of Faraday depth domain be 1/3 or 1/4 of full width half maximum of the rotation measure spread function.