Sparse inversion of Stokes profiles. I. Two-dimensional Milne-Eddington inversions

TL;DR

This paper introduces a novel inversion code for Stokes profiles that leverages sparsity and spatial correlation, improving robustness and contrast in physical parameter inference from spectropolarimetric data.

Contribution

The paper presents a new inversion method using sparsity and proximal algorithms to incorporate spatial correlations, surpassing traditional pixel-by-pixel approaches.

Findings

Enhanced robustness compared to pixel-by-pixel inversions

Ability to compensate for telescope point spread function

Improved contrast in inferred physical parameters

Abstract

Inversion codes are numerical tools used for the inference of physical properties from the observations. Despite their success, the quality of current spectropolarimetric observations and those expected in the near future presents a challenge to current inversion codes. The pixel-by-pixel strategy of inverting spectropolarimetric data that we currently utilize needs to be surpassed and improved. The inverted physical parameters have to take into account the spatial correlation that is present in the data and that contains valuable physical information. We utilize the concept of sparsity or compressibility to develop an new generation of inversion codes for the Stokes parameters. The inversion code uses numerical optimization techniques based on the idea of proximal algorithms to impose sparsity. In so doing, we allow for the first time to exploit the presence of spatial correlation on the maps of physical parameters. Sparsity also regularizes the solution by reducing the number of unknowns. We compare the results of the new inversion code with pixel-by-pixel inversions, demonstrating the increase in robustness of the solution. We also show how the method can easily compensate for the effect of the telescope point spread function, producing solutions with an enhanced contrast.