  Images of the linear polarization of synchrotron radiation around Active
Galactic Nuclei (AGN) identify their projected magnetic field lines and provide
key data for understanding the physics of accretion and outflow from
supermassive black holes. The highest resolution polarimetric images of AGN are
produced with Very Long Baseline Interferometry (VLBI). Because VLBI
incompletely samples the Fourier transform of the source image, any image
reconstruction that fills in unmeasured spatial frequencies will not be unique
and reconstruction algorithms are required. In this paper, we explore
extensions of the Maximum Entropy Method (MEM) to linear polarimetric VLBI
imaging. In contrast to previous work, our polarimetric MEM algorithm combines
a Stokes I imager that uses only bispectrum measurements that are immune to
atmospheric phase corruption with a joint Stokes Q and U imager that operates
on robust polarimetric ratios. We demonstrate the effectiveness of our
technique on 7- and 3-mm wavelength quasar observations from the VLBA and
simulated 1.3-mm Event Horizon Telescope observations of Sgr A* and M87.
Consistent with past studies, we find that polarimetric MEM can produce
superior resolution compared to the standard CLEAN algorithm when imaging
smooth and compact source distributions. As an imaging framework, MEM is highly
adaptable, allowing a range of constraints on polarization structure.
Polarimetric MEM is thus an attractive choice for image reconstruction with the
EHT.
