High-Resolution Linear Polarimetric Imaging for the Event Horizon Telescope

Abstract

Images of the linear polarizations of synchrotron radiation around active galactic nuclei (AGNs) highlight 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 AGNs 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 some 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 only uses 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.

Superresolution Full-polarimetric Imaging for Radio Interferometry with Sparse Modeling

“…For both models, ℓ 1 regularization and CS-CLEAN have a common trend. The minimum errors are achieved at a resolution of ∼30%-50% of the diffraction limit, and then the NRMSEs show a rapid increase in errors at smaller scales, broadly consistent with previous studies on different model images and data products (Chael et al 2016;Akiyama et al 2016). This clearly shows that, on such small scales, the image is no longer sparse and breaks the underlying assumption of both techniques.…”

“…We also plot the NRMSE metric for reconstructed images in the bottom panel, along with the FWHM size of a convolving circular Gaussian beam. The bestcase scenario-the differences from the original input being due solely to a loss of resolution, not to errors in reconstructing the image-is shown by the black curve labeled "Model" following previous work Chael et al 2016). This is calculated by taking the NRMSE between the model image convolved with a circular Gaussian beam with an FWHM and the original (unconvolved) model image.…”

“…First, we employ the normalized root mean square error (NRMSE) metric following Chael et al (2016) and Akiyama et al (2016), defined as…”

“…Pioneering work in this area has made use of transforms to wavelet or curvelet bases, in which the image can be represented sparsely (e.g., Li et al 2011;Carrillo et al 2014;Dabbech et al 2015;Garsden et al 2015). We have taken another approach by adding total variation (TV) regularization (e.g., Wiaux et al 2010;McEwen & Wiaux 2011;Uemura et al 2015;Chael et al 2016), which produces an image that is sparse in its gradient domain. TV regularization has been shown to be effective for imaging with visibility amplitudes and closure phases (e.g., Akiyama et al 2016) in the superresolution regime finer than the diffraction limit.…”

Time Domain Filtering of Resolved Images of Sgr A∗

“…Thus reconstruction of even static images require sophisticated approaches (e.g. Bouman et al 2016;Chael et al 2016). Nevertheless, reconstruction of high time resolution images from incomplete UV-coverage is possible using several newly developed techniques (Johnson et al 2017, submitted).…”