PCA detection and denoising of Zeeman signatures in stellar polarised spectra

TL;DR

This paper presents a PCA-based method for denoising and detecting Zeeman signatures in stellar spectropolarimetric spectra, significantly improving signal-to-noise ratio and aiding magnetic field detection.

Contribution

It introduces an efficient PCA-based denoising technique with a method to select eigenvectors, enhancing spectral line analysis in stellar observations.

Findings

Significant increase in signal-to-noise ratio achieved

Effective detection of magnetic fields in stellar atmospheres

Robustness and computational simplicity of PCA approach

Abstract

Our main objective is to develop a denoising strategy to increase the signal to noise ratio of individual spectral lines of stellar spectropolarimetric observations. We use a multivariate statistics technique called Principal Component Analysis. The cross-product matrix of the observations is diagonalized to obtain the eigenvectors in which the original observations can be developed. This basis is such that the first eigenvectors contain the greatest variance. Assuming that the noise is uncorrelated a denoising is possible by reconstructing the data with a truncated basis. We propose a method to identify the number of eigenvectors for an efficient noise filtering. Numerical simulations are used to demonstrate that an important increase of the signal to noise ratio per spectral line is possible using PCA denoising techniques. It can be also applied for detection of magnetic fields in stellar atmospheres. We analyze the relation between PCA and commonly used well-known techniques like line addition and least-squares deconvolution. Moreover, PCA is very robust and easy to compute.