Sparse vegetation height estimation based on non-local sample selection with generalised inner product

With the assumption of densely distributed vegetation in PolInSAR processing, the height parameters can be inversed by the conventional random volume over ground (RVoG) method. During the procedure of RVoG, the samples used to estimate the PolInSAR coherence are selected directly from the neighbouring areas. However, for sparsely distributed vegetation, the scattering statistics are different from those of densely distributed vegetation. Therefore, the inversion performance will be deteriorated if the samples are selected directly in the neighbouring areas. A new phase-based method is proposed to select samples, whose positions represent the volume scattering pixels, for sparsely distributed vegetation height inversion. By analysing the scattering characteristics of sparsely distributed vegetation, the processing data vector is formulated based on the amplitude-normalised interferograms. With the PolSAR classification, the generalised inner product (GIP) is iteratively used to select the non-local samples based on the formulated phase data vectors, which are utilised for sparsely distributed vegetation height inversion. For the selected sample sets, the vegetation distribution can be approximately regarded as “dense distribution”, and then the vegetation height parameters can be inversed by RVoG method. Compared to the height inversion performance based on different sample selection methods, the effectiveness of the proposed method is validated by the PolSARPro simulated data and the real airborne L-band PolInSAR data.