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Astron. Astrophys. 355, 759-768 (2000)

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5. Conclusion

The above examples of PCA applied to unpolarised intensity and flux profiles, and to polarised Stokes parameter profiles provide strong evidence that the proposed method of PCA inversion is a viable, and potentially much faster, alternative to non-linear least squares inversion of solar and stellar spectral lines. The technique is characterised by strong reduction in dimensionality. In all cases considered we have seen how a small number of eigenprofiles suffice to obtain an accurate linear reconstruction of the data. The eigenprofiles are estimated by the eigenvectors of either the covariance or the correlation matrix of a database of synthetic spectra. A key result is that the coefficients of this reconstruction, the eigenfeatures, are smooth functions of the model parameters used to generate the synthetic database. In practical application to inversion of observed spectra we could take advantage of this smoothness, using spline interpolation to guarantee adequate sampling of the eigenfeature-parameter relationship.

We want to stress the potential of this inversion method to reject models incompatible with the observations. If the residual error in reconstructing an observed profile from the synthetic eigenprofiles exceeds the observational errors, then one can conclude immediately that the model is inadequate. Contrast this with the equivocal discussions found in non-linear least squares inversion methods about whether or not a poor solution is due to being trapped in a local minimum of the error surface.

The method is not expected, however, to improve the results obtained with other inversion methods, but just to be faster and more efficient. In this sense it can be regarded as a first step towards a real-time inversion code. Neural networks trained with synthetic spectra, as done by Gulati et al. (1997), should be considered as the next step. As solar telescopes become more and more automatic, and new high performance telescopes such as the French-Italian THEMIS, in the Canary Islands, become available for routine observations, the problem of analysing the growing quantity of data will be of primary importance. We anticipate that inversion techniques such as the one presented in this paper will be the only way to handle this information explosion.

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© European Southern Observatory (ESO) 2000

Online publication: March 9, 2000