We consider a problem of high-resolution array radar/SAR imaging formalized in terms of a nonlinear ill-posed inverse problem of nonparametric estimation of the power spatial spectrum pattern (SSP) of the random wavefield scattered from a remotely sensed scene observed through a kernel signal formation operator and contaminated with random Gaussian noise. First, the Sobolev-type solution space is constructed to specify the class of consistent kernel SSP estimators with the reproducing kernel structures adapted to the metrics in such the solution space. Next, the “model-free” variational analysis (VA)-based image enhancement approach and the “model-based” descriptive experiment design (DEED) regularization paradigm are unified into a new dynamic experiment design (DYED) regularization framework. Application of the proposed DYED framework to the adaptive array radar/SAR imaging problem leads to a class of two-level (DEED-VA) regularized SSP reconstruction techniques that aggregate the kernel adaptive anisotropic windowing with the projections onto convex sets to enforce the consistency and robustness of the overall iterative SSP estimators. We also show how the proposed DYED regularization method may be considered as a generalization of the MVDR, APES and other high-resolution nonparametric adaptive radar sensing techniques. A family of the DYED-related algorithms is constructed and their effectiveness is finally illustrated via numerical simulations.

Among the objectives of the upcoming space missions Tandem-L and BIOMASS, is the 3-D representation of the global forest structure via synthetic aperture radar (SAR) tomography (TomoSAR). To achieve such a goal, modern approaches suggest solving the TomoSAR inverse problems by exploiting polarimetric diversity and structural model properties of the different scattering mechanisms. This way, the related tomographic imaging problems are treated in descriptive regularization settings, applying modern non-parametric spatial spectral analysis (SSA) techniques. Nonetheless, the achievable resolution of the commonly performed SSA-based estimators highly depends on the span of the tomographic aperture; furthermore, irregular sampling and non-uniform constellations sacrifice the attainable resolution, introduce artifacts and increase ambiguity. Overcoming these drawbacks, in this paper, we address a new multi-stage iterative technique for feature-enhanced TomoSAR imaging that aggregates the virtual adaptive beamforming (VAB)-based SSA approach, with the wavelet domain thresholding (WDT) regularization framework, which we refer to as WAVAB (WDT-refined VAB). First, high resolution imagery is recovered applying the descriptive experiment design regularization (DEDR)-inspired reconstructive processing. Next, the additional resolution enhancement with suppression of artifacts is performed, via the WDT-based sparsity promoting refinement in the wavelet transform (WT) domain. Additionally, incorporation of the sum of Kronecker products (SKP) decomposition technique at the pre-processing stage, improves ground and canopy separation and allows for the utilization of different better adapted TomoSAR imaging techniques, on the ground and canopy structural components, separately. The feature enhancing capabilities of the novel robust WAVAB TomoSAR imaging technique are corroborated through the processing of airborne data of the German Aerospace Center (DLR), providing detailed volume height profiles reconstruction, as an alternative to the competing non-parametric SSA-based methods.

We address a new approach to solving array radar/SAR imaging problems stated and treated as uncertain ill-posed inverse problems of nonparametric estimation of the power spatial spectrum pattern (SSP) of the wavefield scattered from an extended remotely sensed scene via processing the discrete measurements of a finite number of independent observations of the degraded data signals (one realization of the trajectory signal in the case of SAR). The problem is treated in the framework of the worst-case statistical performance optimization-adapted regularization (WOR) method aggregated with descriptive experiment design (DED) paradigm. Our approach is based on the optimization of worst-case statistical performance of the resulting finite-dimensional fused WORDED estimator of the SSP. The DED-formalized projection schemes as well as the weighting "degrees of freedom" of the WOR strategy are incorporated into the optimization procedure subject to the statistical operational worst-case performance constraints imposed on the desired solution operator.

The convex optimization-based descriptive experiment design regularization (DEDR) method is aggregated with the neural network (NN)-adapted variational analysis (VA) approach for adaptive high-resolution sensing into a unified DEDR -VA-NN framework that puts in a single optimization frame high-resolution radar/SAR image formation in uncertain operational scenarios, adaptive despeckling and dynamic scene image enhancement for a variety of sensing modes. The DEDR -VA-NN method outperforms the existing adaptive radar imaging techniques both in resolution and convergence rate. The simulation examples are incorporated to illustrate the efficiency of the proposed DEDR-VA-related imaging techniques.

The robust numerical technique for high-resolution reconstructive imaging and scene analysis is developed as required for enhanced remote sensing with large scale sensor array radar/synthetic aperture radar. The problem-oriented modification of the previously proposed fused Bayesian-regularization (FBR) enhanced radar imaging method is performed to enable it to reconstruct remote sensing signatures (RSS) of interest alleviating problem ill-poseness due to system-level and model-level uncertainties. We report some simulation results of hydrological RSS reconstruction from enhanced real-world environmental images indicative of the efficiency of the developed method.