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. Index Terms-Maximum-likelihood (ML), power spectrum pattern (PSP), spectral analysis (SA), synthetic aperture radar (SAR) tomography (TomoSAR), weighted covariance fitting (WCF). NOMENCLATURE A. List of Acronyms BMR Bayes minimum risk. CLS Constrained least squares. CS Compressed sensing. DOA Direction of arrival. ESPRIT Estimation of signal parameters via rotational invariance techniques. IAA-ML Iterative adaptive approach for ML. LS Least squares.

Single-Look SAR Tomography of Urban Areas

“…The entries of vector s are assumed to be uncorrelated. This simplifies the mathematical developments that factor into the chosen (WISE) statistical regularization approach [12], presented afterward. Therefore, we refer to the same model, with the correlation matrix R s as a diagonal matrix.…”

“…Within the framework of DOA estimation, as in the previous related studies [12][13][14], the considered TomoSAR signal model is defined by the linear equation of observation (EO)…”

“…Here, operator tr{•} retrieves the trace of the embraced matrix. WISE provides an approximate solution to (14), given by (the derivation of (15) is detailed in [12])…”

“…Both MARIA and WISE present similar advantages. The main difference is that WISE is more flexible to the assumed probability density function (pdf) of the observed data [12]; in contrast, MARIA assumes a Gaussian pdf [12,14]. Consequently, taking into account the a priori knowledge about the pdf of the observed data, the most suitable technique is to be chosen.…”

“…The proposed methodology is summarized in Figure 1. For demonstration purposes, in this article, we select DCRCB, which retrieves accurate signal estimates with reduced array output interference [16], and WISE [12], since we assume no a priori information about the pdf of the observed data. The reader, however, can easily adapt the proposed methodology to its convenience.…”