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We consider a set of M images, whose pixel intensities at a common point canbe treated as the components of a M-dimensional vector. We are interested inthe estimation of the modulus of such a vector associated to a compact source.For instance, the detection/estimation of the polarized signal of compactsources immersed in a noisy background is relevant in some fields likeAstrophysics. We develop two different techniques, one based on the MaximumLikelihood Estimator (MLE) applied to the modulus distribution, the modulusfilter (ModF) and other based on prefiltering the components before fusion, thefiltered fusion (FF), to deal with this problem. We present both methods in thegeneral case of M images and apply them to the particular case of three images(linear plus circular polarization). Numerical simulations have been performedto test these filters considering polarized compact sources immersed instationary noise. The FF performs better than the ModF in terms of errors inthe estimated amplitude and position of the source, especially in the lowsignal-to-noise case. We also compare both methods with the direct applicationof a matched filter (MF) on the polarization data. This last technique isclearly outperformed by the new methods.

Filter Design for the Detection/Estimation of the Modulus of a Vector. Application to Polarization Data