  In the recent years, we have seen a rapidly growing number of stellar
magnetic field detections for various types of stars. Many of these magnetic
fields are estimated from spectropolarimetric observations (Stokes V) by using
the so-called center-of-gravity (COG) method. Unfortunately, the accuracy of
this method rapidly deteriorates with increasing noise and thus calls for a
more robust procedure that combines signal detection and field estimation. We
introduce an estimation method that provides not only the effective or mean
longitudinal magnetic field from an observed Stokes V profile but also uses the
net absolute polarization of the profile to obtain an estimate of the apparent
(i.e., velocity resolved) absolute longitudinal magnetic field. By combining
the COG method with an orthogonal-matching-pursuit (OMP) approach, we were able
to decompose observed Stokes profiles with an overcomplete dictionary of
wavelet-basis functions to reliably reconstruct the observed Stokes profiles in
the presence of noise. The elementary wave functions of the sparse
reconstruction process were utilized to estimate the effective longitudinal
magnetic field and the apparent absolute longitudinal magnetic field. A
multiresolution analysis complements the OMP algorithm to provide a robust
detection and estimation method. An extensive Monte-Carlo simulation confirms
the reliability and accuracy of the magnetic OMP approach.
