Adaptive target detection in radar imaging

This thesis addresses a target detection problem in radar imaging for which the co- variance matrix of an unknown Gaussian clutter background has block diagonal structure. This block diagonal structure is the consequence of a target lying along a boundary between two statistically independent clutter regions. We consider three di erent assumptions on knowledge of the clutter covariance structure: both clutter types totally unknown, one of the clutter types known except for its variance, and one of the clutter types completely known. Here we design adaptive detection algorithms using both the generalized likelihood ratio (GLR) and the invariance principles. There has been considerable recent interest in applying invariant hypothesis testing as an alternative to the GLR test. This interest has been motivated by several attractive theoretical properties of invariant tests including: exact robustness to variation of nuisance parameters, possible nite-sample min-max optimality, and distributional robustness, i.e. insensitivity to changes in the underlying probability dis- tribution over a particular class. Furthermore, in some important cases the invariant test gives a reasonable test while the GLR test has worse performance than the trivial coin ip decision rule. By exploiting the known covariance structure, a set of maximal invariants is obtained and compared to the GLR procedure. These maximal invariants are a compression of image data which retain target information while being invariant to clutter parameters. In our deep-hide target detection problem, however, there are regimes for which either of the GLR and the invariant tests can outperform the other. We explore the relative advan- tages of GLR and invariance procedures and their robustness to segmentation errors in the context of this radar imaging and target detection application.