This paper investigates the validity of the random-volume-over-ground (RVoG) scattering model assumption for forest scattering on polarimetric interferometric synthetic aperture radar (PolInSAR) data. The model makes some assumptions about the data and the structure of coherency matrices, namely, the equality of the polarimetric covariance matrices and the affine equivalence of the contracted polarimetric interferometric covariance matrix with a Hermitian matrix. The proposed methodology is divided into two main steps. First, invertible affine transforms (ATs) are studied and proposed as a tool to operate with coherence regions. Based on this analysis, the concept of the trace matrix is introduced as its rank depends on the RVoG model assumption validity. Then, with the objective to consider the effects of speckle noise, we consider a maximum-likelihood (ML) framework, on the hypothesis of data distributed according to the complex Gaussian distribution. Hence, we define the ML estimator (MLE) of the PolInSAR coherency matrix according to the RVoG model assumption and the generalized likelihood ratio test of the model. The validity tests and the MLE are analyzed in terms of simulated and real PolInSAR data, considering P-band and L-band data over tropical and boreal forests.

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