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 toward the sensor, constrained to a reduced number of passes. Moreover, the introduction of artifacts and the increase in the ambiguity levels due to irregular sampling, consequence of nonuniform 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 estimation theory, has been successfully demonstrated in the previous related studies. However, these techniques are constrained to the assumption that the probability density function of the observed data is Gaussian. In this article, in order to solve the ill-posed nonlinear 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 with an outline more similar to the expected one, i.e., recovered using matched spatial filtering 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 WCF-based iterative spectral estimator (WISE). 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 obtained from a forested test site.