Descriptive experiment design unified with worst-case performance optimization-adapted regularization for high-resolution radar/SAR imaging

This paper considers the problem of high-resolution imaging of the environment formalized in terms of a nonlinear ill-posed inverse problem of nonparametric estimation of the power spatial spectrum pattern (SSP) of the wavefield scattered from an extended remotely sensed scene (referred to as the scene image) via processing the discrete measurements of a finite number of independent realizations of the observed degraded radar data signals (one realization of the trajectory signal in the case of SAR). The model-level uncertainties are associated with unknown statistics of perturbations of the signal formation operator (SFO) in turbulent environment. The system-level uncertainties are attributed to the imperfect array calibration, finite dimensionality of measurements, uncontrolled antenna vibrations and random carrier trajectory deviations in the case of SAR. An effective method for SSP reconstruction is therefore proposed by incorporating into the minimum risk (MR) nonparametric spectral estimation strategy the experiment design-motivated constraints of SSP observability/identifiability for the finite-dimensional range continuous-to-discrete SFO algorithmically coupled with descriptive experiment design regularization (DEDR) and unified with worst-case statistical performance optimization approach. The MR objective functional is constrained by this information, and the robust DEDR reconstruction operator applicable to the scenarios with the low-rank uncertain estimated data correlation matrices is found. We also show how this algorithm may be considered generalization of the robust MVDR and the regularized inverse spatial filtering techniques. The efficiency of the developed technique is illustrated via numerical simulations.