Compressed Sensing Radar Imaging: Fundamentals, Challenges, and Advances

Abstract

In recent years, sparsity-driven regularization and compressed sensing (CS)-based radar imaging methods have attracted significant attention. This paper provides an introduction to the fundamental concepts of this area. In addition, we will describe both sparsity-driven regularization and CS-based radar imaging methods, along with other approaches in a unified mathematical framework. This will provide readers with a systematic overview of radar imaging theories and methods from a clear mathematical viewpoint. The methods presented in this paper include the minimum variance unbiased estimation, least squares (LS) estimation, Bayesian maximum a posteriori (MAP) estimation, matched filtering, regularization, and CS reconstruction. The characteristics of these methods and their connections are also analyzed. Sparsity-driven regularization and CS based radar imaging methods represent an active research area; there are still many unsolved or open problems, such as the sampling scheme, computational complexity, sparse representation, influence of clutter, and model error compensation. We will summarize the challenges as well as recent advances related to these issues.

Incorporation of aircraft orientation into automatic target recognition using passive radar

“…Since computing RCS for new observation angles in a method‐of‐moments formulation is easy once the surface current has been computed for a given frequency and incident angle, such codes favour adding observed angles over incident angles. It might be feasible to leverage this property, along with ideas from compressed sensing [45, 46], to alleviate database generation and storage concerns. At microwave frequencies, the current tends to clump at corners, so scattering centre models are useful; at lower frequencies, the current tends to spread throughout the surface [7], so compressed sensing approaches to low‐frequency databases would require new models.…”

Bayesian compressive sensing for synthetic-aperture radar tomography imaging

“…Recently, a Bayesian compressive-sensing (BCS) framework has been introduced into the SAR-imaging field [10,11]. Using the 'sparseness' prior distribution of imaging scene and taking into account the additive noise in the Bayesian formalism, the BCS-based method could provide a better performance than that of the norm-based CS methods, whenever the conditions of low noise levels hold true [12,13].…”

“…However, the 'sparseness' prior distributions used in Refs. [10,11] are nothing but generalized Gaussian and Laplace random models, which represent in fact invalid low-dimensional models [14]. A Cauchy prior distribution has been suggested in Ref.…”

A MIMO-SAR Tomography Algorithm Based on Fully-Polarimetric Data

“…A large number of virtual apertures in the cross-range and elevation directions are beneficial to obtain high-resolution three-dimensional (3D) radar images [4,5,6], but they also result in a high cost and large size of radar systems due to the increase of the number of antenna elements. When the measured target has several scattering centers in an elevation direction, such as airplanes, an affordable array strategy can be adopted: the priority is given to ensuring adequate cross-range virtual apertures for high-resolution two-dimensional (2D) radar images [7], and then a small number of elevation virtual apertures ensure high-resolution 3D radar images by SAR tomography [8,9,10,11,12,13,14,15,16,17,18].…”

“…A distributed compressed sensing (DCS) algorithm based on fully-polarimetric data is proposed in [13,14,15,16] to improve the accuracy of the estimation. However, the CS algorithm suffers from a high computational expense and is hard to extend to fast practice [18]. In [17], a comparison among tomograms obtained in different polarizations is made to analyze how polarimetry can enhance target signatures.…”