The LMMSE polarimetric Wishart vector speckle filter for multilook data and the LMMSE spatial vector filter for correlated pixels in SAR images

The LMMSE vector speckle filters for full polarimetric multilook SAR data and for single channel SAR images using pixels´s spatial correlation are presented. Both are based on the multiplicative speckle model. In the multilook polarimetric filter, the joint distribution of the elements of the sample covariance matrix of the speckle vector is assumed to be a complex Wishart distribution. The Wishart pdf parameters are the look number L and six complex degrees of coherence. The filter output is a despeckled polarimetric feature vector from which a despeckled covariance matrix or Stokes operator matrix can be computed. For usual detected intensity images, the underlying radar reflectivity and the speckle intensity are assumed to be each a spatially correlated random variable. The input vector is an N dimensional vector whose components are the values of N pixels. Compared with the usual scalar isotropic adaptive filters, the vector filter allows a better smoothing of textured areas by taking into account the spatial correlation of the speckle and of the scene in various directions