Theory and simulation of statistical representation of the Stokes parameters in multilook fields based on polarization basis transformation

A novel analytical representation of polarimetric Stokes parameters´ distributions and their lower-order statistics are derived via the joint Wishart distribution of the covariance matrix of the stochastic multi-look speckle fields by using the polarization basis transformation. The last three Stokes parameters are expressed as a universal form by three parameters of the number samples, the degree of polarization and the polarization weight, which is an extension and generalization of R. Touzi and Y.Q. Jin by considering multiple look radar images, and can be used directly to describe the radiometric data in low resolution radar with polarimetric capabilities. The physical meanings of Stokes parameters via polarization basis transformation bring a short cut for solving the probability density function (PDF) of Stokes parameters. The simulated and experimental data are calculated to justify the expressions derived by us, which provide an excellent match with the novel representation. The conclusion can be useful to speckle reduced, classification and target recognition in complex environments or other applications.