# Super-resolution Full Polarimetric Imaging for Radio Interferometry with Sparse Modeling

## TL;DR

This paper introduces a sparse modeling technique for radio interferometry that achieves super-resolution full polarization imaging, surpassing traditional methods in resolution and fidelity, demonstrated through simulations of M87 with the EHT.

## Contribution

The paper presents a novel sparse modeling approach using combined $ extit{l}_1$ and TV regularization for super-resolution full-polarimetric imaging in radio interferometry.

## Key findings

- Achieves 25-30% of diffraction limit resolution.
- Outperforms CLEAN and single regularization methods.
- Provides higher image fidelity across multiple scales.

## Abstract

We propose a new technique for radio interferometry to obtain super-resolution 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 $\ell _1$-norm and 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 (EHT). We confirm that $\ell _1$+TV regularization can achieve an optimal resolution of $\sim 25-30$\% of the diffraction limit $\lambda/D_{\rm max}$, which is the nominal spatial resolution of a radio interferometer for both the total intensity (i.e. Stokes $I$) and linear polarizations (i.e. Stokes $Q$ and $U$). This optimal resolution is better than that obtained from the widely used Cotton-Schwab CLEAN algorithm or from using $\ell _1$ or TV regularizations alone. Furthermore, we find that $\ell _1$+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 super-resolution 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.