Statistical Regularization for Enhanced TomoSAR Imaging

Abstract

One of the main topics in synthetic aperture radar (SAR) tomography (TomoSAR) is the estimation of the vertical structures’ location, which scatter the field back towards the sensor, constrained to a reduced number of passes. Moreover, the introduction of artifacts and the increase of the ambiguity levels due to irregular sampling, consequence of non-uniform acquisition constellations, complicate the accurate estimation of the source parameters. Pursuing the alleviation of such drawbacks, the use of statistical regularization approaches, based on the maximum-likelihood (ML) estimation theory, has been successfully demonstrated in the previous related studies. However, these techniques are constrained to the assumption that the probability density function (pdf) of the observed data is Gaussian. In this paper, in order to solve the ill-posed non-linear TomoSAR inverse problem, we relax this assumption and apply the weighted covariance fitting (WCF) criterion instead. The latter alleviates the previously mentioned drawbacks, and retrieves a power spectrum pattern (PSP) with an outline more similar to the expected one, i.e., recovered using matched spatial filtering (MSF) with a higher number of tracks. First, we present the mathematical background of the related regularization methods, adapted to solve the TomoSAR inverse problem, from which we derive our novel technique, named WISE (WCF-based Iterative Spectral Estimator). Then, the differences and similarities between the addressed regularization approaches are discussed, besides their main advantages and disadvantages. Finally, the implementation details of WISE are treated, along with simulated examples and experimental results gotten from a forested test site.