Optimal Bayesian texture estimators for speckle filtering of detected and polarimetric data

For surfaces satisfying the “product model”, the sample covariance matrix (CM) is the product of a positive scalar random variable μ representing texture and a mean CM representing the polarimetric properties of the surface. The maximum likelihood (ML) estimator of μ is given by the multilook polarimetric whitening filter (MPWF). The ML estimator satisfies the well known multiplicative speckle model. For the multiplicative model, the authors analyze the optimality of the texture estimators by using decision theory and Bayes approach. They develop a new estimator for gamma distributed texture. The a posteriori mean (APM) estimator is radiometrically unbiased and has the smallest mean square error (MSE) of all estimators. The gamma-MAP estimator, on the contrary, is radiometrically biased, but it preserves the textural contrast better