In the recent years, we have seen a rapidly growing number of stellarmagnetic field detections for various types of stars. Many of these magneticfields are estimated from spectropolarimetric observations (Stokes V) by usingthe so-called center-of-gravity (COG) method. Unfortunately, the accuracy ofthis method rapidly deteriorates with increasing noise and thus calls for amore robust procedure that combines signal detection and field estimation. Weintroduce an estimation method that provides not only the effective or meanlongitudinal magnetic field from an observed Stokes V profile but also uses thenet absolute polarization of the profile to obtain an estimate of the apparent(i.e., velocity resolved) absolute longitudinal magnetic field. By combiningthe COG method with an orthogonal-matching-pursuit (OMP) approach, we were ableto decompose observed Stokes profiles with an overcomplete dictionary ofwavelet-basis functions to reliably reconstruct the observed Stokes profiles inthe presence of noise. The elementary wave functions of the sparsereconstruction process were utilized to estimate the effective longitudinalmagnetic field and the apparent absolute longitudinal magnetic field. Amultiresolution analysis complements the OMP algorithm to provide a robustdetection and estimation method. An extensive Monte-Carlo simulation confirmsthe reliability and accuracy of the magnetic OMP approach.
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