Optimal speckle reduction for the product model in multilook polarimetric SAR imagery and the Wishart distribution

Several optimal techniques exist to reduce speckle effects on polarimetric data, e.g. the Linear Minimum Mean Square Error (LMMSE) vector filter for multilook detected data or optimum summations such as the Polarimetric Whitening Filter (PWF) for one look complex data. Among other drawbacks, these standard methods do not preserve full polarimetric data, or they do not use the a priori texture distribution, or they are restricted to one look data. In the simplified case of data satisfying the so-called “product model”, new optimal techniques are described in this paper that are able to reduce speckle effects on multilook data, while preserving fully polarimetric information and texture variations. This “product model” is valid when the scene texture has a large scale of variation and is polarization independent, for instance in K-distributed clutter. Under this assumption, the measured covariance matrix (multilook data) is the product of a scalar random variable μ (the texture) and the covariance matrix C_zh of an equivalent Gaussian homogeneous surface. C_zh is the mean covariance matrix and contains the polarimetric information. A PWF for multilook complex data (MPWF) is proposed and is shown to be related to optimal statistical estimators of the texture (Maximum Likelihood, Maximum A Posteriori, MMSE…) when the complex Wishart distribution is used. The ML estimation of C _zh for textured areas is given and the adaptive filters based on these new tools are described. The results indicate a large speckle reduction. Moreover, the mean values of polarimetric features such as the magnitude and the phase of the HH-VV complex degree of coherence are preserved