Solving Enhanced Radar Imaging Inverse Problems: From Descriptive Regularization to Feature Structured Superresolution Sensing

Resolution enhancement (RE) and superresolution (SR) enhancement of the remote sensing imagery provided by conventional low-resolution (LR) coherent real aperture radar or fractional SAR sensors operating in real-world scenarios with the model data statistics unknown to the observer belong to a class of nonlinear uncertain inverse problems. The classical Bayesian statistical inference and modern compressed sensing-based approaches are not properly adapted to such inverse problems as the latter require robust spatially selective image despeckling adaptively balanced over RE with preservation of salient radar/SAR image features. In this paper, we propose to treat the RE/SR radar imaging inverse problems in a multistage descriptive experiment design regularization (DEDR) setting that logically unifies composite RE optimization tasks into a four-level structured DEDR framework. First, the conventional despeckled LR image formed via performing the matched spatial filtering of the recorded trajectory signals is considered as initial LR data for further feature enhanced processing. Second, the minimum risk inspired robust adaptive beamforming method is DEDR restructured and unified with the convergence guaranteed and sparsity promoting composite projections onto convex sets aimed at feature enhanced recovery of the high-resolution despeckled image. The third level suggests transition to the nested refined SR scales with preservation of the consistency space. Finally, the SR recovery of the fine image features is performed consequently in each nested refined image frame via discrete wavelet domain postprocessing-based sparsity promoting denoising with consistency preservation. The new multistage SR-DEDR technique conjugates excellent despeckling and SR enhancement performances corroborated via reported computer simulations.