Determination Of Faraday Rotation Measure Based On Compressive Sensing

Faraday rotation measure synthesis(RMS)is one of the most powerful tools to study cosmic magnetic field.Faraday dispersion function(FDF),polarized intensity as a function of Faraday depth,is derived from polarization observation based on the Fourier relation between FDF and observed polarization in this method.However,due to the limitation of observation wavelength coverage,the FDF obtained by this method is ill-conditioned.It is therefore necessary to find a more reliable method to reconstruct FDF.Compressive sensing/sampling(CS)is a new technology in the field of signal processing,the advantage of this technique is that it is possible to achieve better approximation of signals from a small amount of data in contrast with traditional methods.Recently,the CS algorithm has been proposed to recover FDFs,and has been claimed to be better than RMS.In this thesis,we mainly benchmark the feasibility of the method for reconstructing FDF based on CS with actual observation frequency,and explore how to set relevant parameters in actual application.We find that the reconstructed results of FDF based on CS are influenced by various factors,such as noise,the separation of different emitting components in Faraday depth domain and the polarized intensity of these components and so on.In a large sample of experiments,we performed least square fitting around the peak of the reconstruction results,and the fitted Faraday depth is closer to the true values.We suggest that ??(the resolution in Faraday depth domain).be 1/4 of ??FWHM(full width half maximum of the rotation measure spread function)for frequency range 1.1-3.1GHz;?? be 1/9 of ??FWHM for frequency range 1.1-4.1 GHz;and ?? be 1/41/5.,1/7 or 1/8 of ??FWHM for frequency range 2-4GHz.We suggest that a wider wavelength range be used in practical applications.