Comparison of Local and Non-Local Methods in Covariance Matrix Estimation by Using Multi-baseline SAR Interferometry and Height Extraction for Principal Components with Maximum Likelihood Approach

By today, the technology of synthetic aperture radar (SAR) interferometry (InSAR) has been largely exploited in digital elevation model (DEM) generation and deformation mapping. Conventional InSAR technique exploits two SAR images acquired from slightly different angles, in which the information of elevation and deformation can be captured through processing of the phase difference of the images called interferometric phase. Depart from undeniable efficiency of interferometric SAR processing technique (InSAR), some main issues such as phase unwrapping ambiguity may limit its applications and its accuracy in height mapping. However, in the frame of multi-baseline interferometry and by the availability of more than one interferogram of the same region these problems can be overcome. Multi-baseline SAR interferometry are hence of great interest and can be successfully exploited for automatic phase unwrapping and high quality DEM reconstruction. This paper focuses on stacks of interferometric SAR data as they are used as input to multi-baseline framework for the purpose of height estimation and compare the results of such local and non- local covariance matrix estimation methods achieved by same data and on the same area, where the information of estimated covariance matrix is employed in the elevation mapping. In local methods such as Boxcar, a fixed-size window is considered for the central pixel which do not consider the statistical homogeneity of neighboring pixels, so this method in non-homogenous area leads the results to lower accuracy. In non-local methods the procedure is centered around the idea of checking the pixels to find the same statistical distribution as the investigated pixel, which is realized by Wishart similarity function. In this case, all the similar pixels are then used to estimate the complex covariance matrix of the reference pixel. In the context of non-local filtering, one of the most efficient method is NLSAR approach, which has been considered in our framework. More precisely, NLSAR uses samples in a search window and assigns each pixel a weight based on its similarity to the target pixel. The idea of NLSAR approach is to find, within a search window, for each pixel p to be filtered non-local neighbors t that share statistical similarity with the considered pixel. A pixel t is assumed to come from the same statistical population as the considered pixel p, if the patches or local neighbors that surround the two pixels are similar. The similarity for two pixels is defined as a likelihood-ratio test based on the hypothesis that their two Wishart distributed covariance matrices are equal. The main peculiarity that made the NLSAR approach extremely popular is its ability of filtering noise while preserving structures and discontinuities. The stadium height estimated by using the covariance matrix estimated with Boxcar and NLSAR methods respectivey is equal to 41.100 and 42.5400 meter which in the comparison with the actual height extracted from AfriSAR mission, indicates higher accuracy for the results of NLSAR method. The task of covariance matrix estimation is so challenging for complex area such as the area used for this paper which contains the Angondjé stadium in Mondah, Gabon, that represented a complex scenario because of the occurrence of layover, a phenomenon that gives rise to the interference within the same pixel of ground scattering mechanisms located of different height with  same slant range distance. we use PCA (Principal Component Analysis) to decompose principal scattering mechanisms. Then , the powerful statistics Maximum Likelihood (ML) technique is used to properly compute the elevation information of the principal components by the available information of covariance matrix. From this covariance matrix, both amplitude and interferometric phase values extracted which are then used for height estimation.