An Information-Theoretic Detector for Multiple Scatterers in SAR Tomography

TL;DR

This paper tackles the challenge of detecting multiple scatterers within the same TomoSAR resolution cell by introducing a one-stage, information-theoretic detector (KLIC-D) that uses a single adaptive threshold to handle an unknown number of scatterers. A two-step approach combines compressive sensing to estimate sparse elevation-velocity-position support with a Kullback-Leibler Information Criterion-based decision rule, yielding a CFAR detector that scales beyond two scatterers. Compared to the Sup-GLRT, KLIC-D achieves similar detection/estimation performance while reducing computational burden and providing straightforward threshold design, demonstrated on synthetic data and COSMO-SkyMed real data from Naples. The method offers practical advantages for high-rise urban scenes and lays groundwork for extensions to more complex interference models and two-stage architectures.

Abstract

Persistent scatterer interferometry and Synthetic Aperture Radar (SAR) Tomography are powerful tools for the detection and time monitoring of persistent scatterers. They have been proven to be effective in urban scenarios, especially for buildings and infrastructures 3-D reconstruction and monitoring of deformation. In urban areas, occurrence of layover leads to the presence of multiple contributions within the same image pixel from scatterers located at different heights. In the context of SAR Tomography, this problem can be addressed by considering a multiple hypothesis test to detect the presence of feasible multiple scatterers [1][2]. In the present paper, we consider this problem in the framework of the information theory and exploit the theoretical tool, developed in [3], to design a one-stage adaptive architecture for multiple hypothesis testing problems in the context of SAR Tomography. Moreover, we resort to the compressive sensing approach for the estimation of the unknown parameters under each hypothesis. This architecture has been verified on both simulated as well as real data also in comparison with suitable counterparts.

Figures (22)

• Figure 1: Multi-temporal tomographic SAR geometry, with the radar acquiring from different positions separated by $b_n$, $n=1,...,N$; $\theta$ is the look angle, $s$ is the elevation direction (orthogonal to the line-of-sight $r$).
• Figure 2: Block scheme for the proposed multiple hypothesis test.
• Figure 3: Distribution of the acquisitions, reported as stars, in the Temporal / Spatial Baseline domain.
• Figure 4: Relative variation of the log-likelihood \ref{['maximization_equation']} versus the number of iterations for the compressive sensing algorithm.
• Figure 5: Sensitivity analysis of $P_{fa}$ a with respect to mismatched $\sigma^2$ parameter (threshold is estimated with $\sigma^2=1$).