We address the problem of estimating the polarization degree of polarimetric images in coherent illumination. It has been recently shown that the degree of polarization associated with polarimetric images can be estimated by the method of moments applied to two or four images assuming fully developed speckle. We show that the estimation can also be conducted by using maximum likelihood methods. The maximum likelihood estimators of the polarization degree are derived from the joint distribution of the image intensities. We show that the joint distribution of polarimetric images is a multivariate gamma distribution whose marginals are univariate, bivariate, or trivariate gamma distributions. This property is used to derive maximum likelihood estimators of the polarization degree using two, three, or four images. The proposed estimators provide better performance than the estimators of moments. These results are illustrated by estimations conducted on synthetic and real images.
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