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Our main objective is to develop a denoising strategy to increase the signalto noise ratio of individual spectral lines of stellar spectropolarimetricobservations.  We use a multivariate statistics technique called Principal ComponentAnalysis. The cross-product matrix of the observations is diagonalized toobtain 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 byreconstructing the data with a truncated basis. We propose a method to identifythe number of eigenvectors for an efficient noise filtering.  Numerical simulations are used to demonstrate that an important increase ofthe signal to noise ratio per spectral line is possible using PCA denoisingtechniques. It can be also applied for detection of magnetic fields in stellaratmospheres. We analyze the relation between PCA and commonly used well-knowntechniques like line addition and least-squares deconvolution. Moreover, PCA isvery robust and easy to compute.

PCA detection and denoising of Zeeman signatures in stellar polarised spectra