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

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Fast inversion of spectral lines using principal component analysis

I. Fundamentals

D.E. Rees 1, A. López Ariste 2, J. Thatcher 3 and M. Semel 2

1 CSIRO Telecommunications and Industrial Physics, P.O. Box 76, Epping NSW 1710, Australia
2 DASOP, URA 326, Observatoire de Paris, Section de Meudon
3 Southern Sydney Institute of TAFE, Hotham Rd., Gymea NSW 2227, Australia

Received 25 August 1999 / Accepted 18 November 1999

Abstract

This paper presents PCA inversion, a novel application of Principal Component Analysis to the problem of spectral line inversion , ie. solar/stellar atmospheric model parameter estimation from spectral lines. For a given type of spectral line we compute a database of synthetic spectral profiles using a large number of models. Inversion of an observed profile to obtain an atmospheric model is equivalent to a problem in pattern recognition, finding the nearest profile in the synthetic profile database. To reduce dimensionality we use the synthetic data as a PCA training set to decompose each synthetic (and observed) profile into a sum of a small number of principal components, or eigenprofiles. The coefficients of this decomposition can be regarded as elements of a low-dimensional eigenfeature vector. The eigenfeatures are smooth functions of model parameters, indicating that eigenfeatures for parameters not in the training set could be easily estimated by interpolation. Search for the nearest profile is fast because it is done in the eigenfeature vector space. We illustrate the method using several types of synthetic spectra: unpolarised intensity profiles of a line formed in a Milne-Eddington model atmosphere; unpolarised H[FORMULA] flux profiles of a line formed in non-Local Thermodynamic Equilibrium in the chromosphere of a cool star; and polarised Stokes parameter profiles of a line split by the Zeeman effect in the presence of a magnetic field. We also apply PCA to a set of Stokes data observed in a sunspot region by the High Altitude Observatory Advanced Stokes Polarimeter. PCA inversion is proposed as a fast alternative to non-linear least squares inversion commonly used for solar magnetic field measurements based on such Stokes data.

Key words: line: profiles – methods: data analysis – methods: numerical

Send offprint requests to: A. López Ariste

Correspondence to: Arturo.Lopez@obspm.fr

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© European Southern Observatory (ESO) 2000

Online publication: March 9, 2000
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