Several problems arising in electromagnetics can be directly formulated or suitably recast for an effective solution within the compressive sensing (CS) framework. This has motivated a great interest in developing and applying CS methodologies to several conventional and innovative electromagnetic scenarios. This work is aimed at presenting, to the best of the authors knowledge, a review of the state-of-the-art and most recent advances of CS formulations and related methods as applied to electromagnetics. Toward this end, a wide set of applicative scenarios comprising the diagnosis and synthesis of antenna arrays, the estimation of directions of arrival, and the solution of inverse scattering and radar imaging problems are reviewed. Current challenges and trends in the application of CS to the solution of traditional and new electromagnetic problems are also discussed.

Compressive Sensing in Electromagnetics - A Review

An innovative array diagnosis technique based on a compressive-sensing (CS) paradigm is introduced in the case of linear arrangements. Besides detecting the faulty elements, the approach is able to provide the degree of reliability of such an estimation. Starting from the measured samples of the far-field pattern, the array diagnosis problem is formulated in a Bayesian framework and it is successively solved with a fast relevance vector machine (RVM). The arising Bayesian compressive sensing (BCS) approach is numerically validated through a set of representative examples aimed at providing suitable user's guidelines as well as some insights on the method features and potentialities.

Reliable Diagnosis of Large Linear Arrays—A Bayesian Compressive Sensing Approach

For inverse synthetic aperture radar imagery, the inherent sparsity of the scatterers in the range-Doppler domain has been exploited to achieve a high-resolution range profile or Doppler spectrum. Prior to applying the sparse recovery technique, preprocessing procedures are performed for the minimization of the translational-motion-induced Doppler effects. Due to the imperfection of coarse motion compensation, the autofocus technique is further required to eliminate the residual phase errors. This paper considers the phase error correction problem in the context of the sparse signal recovery technique. In order to encode sparsity, a multitask Bayesian model is utilized to probabilistically formulate this problem in a hierarchical manner. In this novel method, a focused high-resolution radar image is obtained by estimating the sparse scattering coefficients and phase errors in individual and global stages, respectively, to statistically make use of the sparsity. The superiority of this algorithm is that the uncertainty information of the estimation can be properly incorporated to obtain enhanced estimation accuracy. Moreover, the proposed algorithm achieves guaranteed convergence and avoids a tedious parameter-tuning procedure. Experimental results based on synthetic and practical data have demonstrated that our method has a desirable denoising capability and can produce a relatively well-focused image of the target, particularly in low signal-to-noise ratio and high undersampling ratio scenarios, compared with other recently reported methods.

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An Autofocus Technique for High-Resolution Inverse Synthetic Aperture Radar Imagery

This paper presents a novel inverse synthetic aperture radar (ISAR) imaging method by exploiting the inherent continuity of the scatterers on the target scene to obtain enhanced target images within a Bayesian framework. A simplified radar system is utilized by transmitting the sparse probing frequency signal, where the ISAR imaging problem can be converted to deal with underdetermined linear inverse scattering. Following the Bayesian compressive sensing (BCS) theory, a hierarchical Bayesian prior is employed to model the scatterers in the range-Doppler plane. In contrast to the independent prior on each scatterer in the conventional BCS, a correlated prior is proposed to statistically encourage the continuity structure of the scatterers in the target region. To overcome the intractability of the posterior distribution, the Gibbs sampling strategy is used for Bayesian inference. The parameters of the signal model are inferred efficiently from samples obtained by the Gibbs sampler. Because the proposed method is a data-driven learning process, the tedious parameter tuning process required by the convex optimization-based approaches can be avoided. Both the synthetic and the experimental results demonstrate that the proposed algorithm can achieve substantial improvements in the scenarios of limited measurements and low signal-to-noise ratio compared with other reported algorithms for ISAR imaging problems.

https://dr.ntu.edu.sg/bitstream/10356/104851/1/Enhanced%20ISAR%20Imaging%20by%20Exploiting%20the%20Continuity%20of%20the%20Target%20Scene.pdf

Enhanced ISAR Imaging by Exploiting the Continuity of the Target Scene

To encourage the continuity of the target scene, a novel sparse representation (SR)-based inverse synthetic aperture radar (ISAR) imaging algorithm is proposed by leveraging the Markov random fields (MRF). The ISAR imaging problem is reformulated in a Bayesian framework where correlated priors are used for the hidden variables to enforce the continuity of target scene. To further enforce the nonzero or zero scatterers to cluster in a spatial consistent manner, the MRF is used as the prior for the support of the target scene. To surmount the difficulty of calculating the posterior due to the imposed correlated priors and the MRF, variational Bayes expectation-maximization (VBEM) method is used to simultaneously approximate the posterior of the hidden variables and estimate the model parameters of the MRF. The convergence of the method is easily diagnosed by commonly used stopping criterion. Both the synthetic and the experimental results demonstrate that the proposed algorithm can achieve substantial improvements in terms of preserving the weak scatterers and removing noise components over other reported SR-based ISAR imaging algorithms.

Sparse Representation-Based ISAR Imaging Using Markov Random Fields

To achieve high-resolution two dimension images, synthetic aperture radar (SAR) with ultra wide-band faces considerably technical challenges such as long data collection time, huge amount of data storage and high hardware complexity In these years, several imaging modalities based on compressive sensing (CS) have been proposed which can provide high-resolution images using significantly reduced number of samples However, the CS-based methods are sensitive to noise and clutter In this study, a new imaging modality based on Bayesian compressive sensing (BCS) is proposed along with a novel compressed sampling scheme Clutter, which the previous CS-based methods not considered, is also included in this study This new imaging scheme requires minor change to traditional system and allows both range and azimuth compressed sampling Also, the Bayesian formalism accounts for additive noise encountered in the compressed measurement process Experiments are carried out with noisy and cluttered imaging scenes to verify the new imaging scheme The results indicate that the Bayesian formalism can provide a sharp and sparse image absence of side-lobes, which is the common problem in conventional imaging methods and has fewer artifacts compared with the previous version of CS-based methods

Y. Pi

Papers

Bayesian compressive sensing in synthetic aperture radar imaging