Filter Design for the Detection/Estimation of the Modulus of a Vector.
  Application to Polarization Data
  We consider a set of M images, whose pixel intensities at a common point can
be treated as the components of a M-dimensional vector. We are interested in
the estimation of the modulus of such a vector associated to a compact source.
For instance, the detection/estimation of the polarized signal of compact
sources immersed in a noisy background is relevant in some fields like
Astrophysics. We develop two different techniques, one based on the Maximum
Likelihood Estimator (MLE) applied to the modulus distribution, the modulus
filter (ModF) and other based on prefiltering the components before fusion, the
filtered fusion (FF), to deal with this problem. We present both methods in the
general case of M images and apply them to the particular case of three images
(linear plus circular polarization). Numerical simulations have been performed
to test these filters considering polarized compact sources immersed in
stationary noise. The FF performs better than the ModF in terms of errors in
the estimated amplitude and position of the source, especially in the low
signal-to-noise case. We also compare both methods with the direct application
of a matched filter (MF) on the polarization data. This last technique is
clearly outperformed by the new methods.
