Superresolution Full-polarimetric Imaging for Radio Interferometry with Sparse Modeling

<jats:title>Abstract</jats:title> <jats:p>We propose a new technique for radio interferometry to obtain superresolution full-polarization images in all four Stokes parameters using sparse modeling. The proposed technique reconstructs the image in each Stokes parameter from the corresponding full-complex Stokes visibilities by utilizing two regularization functions: the <jats:italic>ℓ</jats:italic> <jats:sub>1</jats:sub> norm and the total variation (TV) of the brightness distribution. As an application of this technique, we present simulated linear polarization observations of two physically motivated models of M87 with the Event Horizon Telescope. We confirm that <jats:italic>ℓ</jats:italic> <jats:sub>1</jats:sub>+TV regularization can achieve an optimal resolution of ∼25%–30% of the diffraction limit <jats:inline-formula> <jats:tex-math> <?CDATA $\lambda /{D}_{\max }$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ajaa6302ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>, which is the nominal spatial resolution of a radio interferometer for both the total intensity (i.e., Stokes <jats:italic>I</jats:italic>) and linear polarizations (i.e., Stokes <jats:italic>Q</jats:italic> and <jats:italic>U</jats:italic>). This optimal resolution is better than that obtained from the widely used Cotton–Schwab CLEAN algorithm or from using <jats:italic>ℓ</jats:italic> <jats:sub>1</jats:sub> or TV regularizations alone. Furthermore, we find that <jats:italic>ℓ</jats:italic> <jats:sub>1</jats:sub>+TV regularization can achieve much better image fidelity in linear polarization than other techniques over a wide range of spatial scales, not only in the superresolution regime, but also on scales larger than the diffraction limit. Our results clearly demonstrate that sparse reconstruction is a useful choice for high-fidelity full-polarimetric interferometric imaging.</jats:p>