  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.
