From Matched Spatial Filtering towards the Fused Statistical Descriptive Regularization Method for Enhanced Radar Imaging

Abstract

We address a new approach to solve the ill-posed nonlinear inverse problem of high-resolution numerical reconstruction of the spatial spectrum pattern (SSP) of the backscattered wavefield sources distributed over the remotely sensed scene. An array or synthesized array radar (SAR) that employs digital data signal processing is considered. By exploiting the idea of combining the statistical minimum risk estimation paradigm with numerical descriptive regularization techniques, we address a new fused statistical descriptive regularization (SDR) strategy for enhanced radar imaging. Pursuing such an approach, we establish a family of the SDR-related SSP estimators, that encompass a manifold of existing beamforming techniques ranging from traditional matched filter to robust and adaptive spatial filtering, and minimum variance methods.

Intelligent Experiment Design-Based Virtual Remote Sensing Laboratory

“…In the DEDR framework developed originally in [8], [10], [11] complex multisensor measurement data wavefields in the observation domain are modeled as operator transforms of the initial scene scattering fields degraded by clutter and noise. The formalism of such transforms is specified by the corresponding uncertain signal formation operator (SFO) models derived from scattering theory [2], [4].…”

“…In [8], [10], [11], we followed a generalized maximum entropy (ME) formalization of a priori information regarding the spatial spectrum patterns (SSPs) of the scattered wavefields that unify diverse RS imaging problem settings. Being nonlinear and solution-dependent, the optimal general-form DEDR estimators of the SSPs constructed in [8], [10] require computationally intensive adaptive signal processing operations that involve also the proper construction of the regularizing projections onto convex (solution) sets (POCS) ruled by the adopted fixed-point contractive iteration process. The fused KB DEDR algorithm design methodology [11] aggregates next the ME method with the diverse regularization and KB post-processing considerations.…”

“…Following [6], [8], [10] the DEDR is addressed to as a methodology that unifies the family of the previously developed nonparametric high-resolution RS imaging techniques. Such unified formalism allows involving into the DEDR different convex regularization and neural computation paradigms (e.g., the POCS regularization and KB method fusion) that enables the end user to modify the existing techniques via incorporation of some controllable algorithmic-level "degrees of freedom" as well as design a variety of efficient aggregated/fused data/image processing methods.…”

“…Such unified formalism allows involving into the DEDR different convex regularization and neural computation paradigms (e.g., the POCS regularization and KB method fusion) that enables the end user to modify the existing techniques via incorporation of some controllable algorithmic-level "degrees of freedom" as well as design a variety of efficient aggregated/fused data/image processing methods. The data/image processing tasks that may be performed applying the DEDR methodology can be mathematically formalized in the terms of the following unified optimization problem [8], [10]. …”

“…m = 1, …, M, where F (m) represent the system/method degradation operators usually referred to as the imaging system point spread functions (PSF), and vectors n (m) represent composite noises (usually with unknown statistics) in the actually acquired images, respectively. Different RS imaging methods incorporate different definitions for corresponding employed objective (cost) functions {J m (v)} [2], [3], [5], [6], [8], [10]. For the deterministic constrained least squares (CLS) method [2], [3]…”