Nonlocal Filtering Applied to 3-D Reconstruction of Tomographic SAR Data

In this paper, we introduce two spatially adaptive filtering methods to improve the estimation of the covariance matrix (CM), which is required for the processing of tomographic SAR data. We evaluate their effect on scatterer separation and height estimation. We propose several criteria to evaluate such methods and introduce a spatial simulation procedure allowing generating a tomographic image stack from a 3-D building model, assuming a multitrack airborne configuration and a distributed target model incorporating multidimensional speckle. Inversion of such a model requires the estimation of a CM from the data. Consequently, we propose two nonlocal methods to improve the estimation of the CM. The first one was previously introduced for polarimetric data and uses pixel similarities based on Riemannian distances between CMs. The second one is a new method extending the previous one to similarities between patches. We show the importance of spatial adaptivity in covariance estimation by comparing the 3-D reconstructions obtained with our filters and other methods. Further experiments on simulated and L-band experimental data show the ability of the nonlocal filters to improve the height estimation and scatterer separation in layover areas thanks to their smoothing and edge-preserving properties.