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Astron. Astrophys. 355, 759-768 (2000)
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]](img1.gif)
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
Contents
- 1. Introduction
- 2. PCA inversion
- 3. PCA of unpolarised spectra
- 3.1. Intensity profiles
- 3.2. H flux profiles
- 4. PCA of polarised spectra
- 4.1. Synthetic Stokes data
- 4.2. Observed Stokes data
- 5. Conclusion
- Acknowledgements
- References
© European Southern Observatory (ESO) 2000
Online publication: March 9, 2000
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