The electromagnetic scattering problem over a wide incident angle can be rapidly solved by introducing the compressive sensing theory into the method of moments, whose main computational complexity is comprised of two parts: a few calculations of matrix equations and the recovery of original induced currents. To further improve the method, a novel construction scheme of measurement matrix is proposed in this paper. With the help of the measurement matrix, one can obtain a sparse sensing matrix, and consequently the computational cost for recovery can be reduced by at least half. The scheme is described in detail, and the analysis of computational complexity and numerical experiments are provided to demonstrate the effectiveness.

Compressed sensing allows recovery of image signals using a portion of data – a technique that has drastically revolutionized the field of through-the-wall radar imaging (TWRI). This technique can be accomplished through nonlinear methods, including convex programming and greedy iterative algorithms. However, such (nonlinear) methods increase the computational cost at the sensing and reconstruction stages, thus limiting the application of TWRI in delicate practical tasks (e.g. military operations and rescue missions) that demand fast response times. Motivated by this limitation, the current work introduces the use of a numerical optimization algorithm, called Limited Memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS), to the TWRI framework to lower image reconstruction time. LBFGS, a well-known Quasi-Newton algorithm, has traditionally been applied to solve large scale optimization problems. Despite its potential applications, this algorithm has not been extensively applied in TWRI. Therefore, guided by LBFGS and using the Euclidean norm, we employed the regularized least square method to solve the cost function of the TWRI problem. Simulation results show that our method reduces the computational time by 87% relative to the classical method, even under situations of increased number of targets or large data volume. Moreover, the results show that the proposed method remains robust when applied to noisy environment.

This paper presents two modifications of compressive sensing (CS)-based approach applied to the near-field diagnosis of active phased arrays. CS-based antenna array diagnosis allows a significant reduction of measurement time, which is crucial for the characterization of electrically large active antenna arrays, e.g. used in synthetic aperture radar. However, practical implementation of this method is limited by two factors: first, it is sensitive to thermal instabilities of the array under test, and second, excitation reconstruction accuracy strongly depends on the accuracy of the elements of the measurement matrix. First proposed modification allows taking into account of thermal instability of the array by using an iterative ℓ1-minimization procedure. The second modification increases the accuracy of reconstruction using several simple additional measurements.

The $l_{0}$-minimisation problem has attracted much attention in recent years with the development of compressive sensing. The spark of a matrix is an important measure that can determine whether a given sparse vector is the solution of an $l_{0}$-minimisation problem. However, its calculation involves a combinatorial search over all possible subsets of columns of the matrix, which is an NP-hard problem. We use Weyl’s theorem to give two new lower bounds for the spark of a matrix. One is based on the mutual coherence and the other on the coherence function. Numerical examples are given to show that the new bounds can be significantly better than existing ones.

Compressive Sensing is an emerging technology for data compression and simultaneous data acquisition. This is an enabling technique for significant reduction in data bandwidth, and transmission power and hence, can greatly benefit space-flight instruments. We apply this process to detect exoplanets via gravitational microlensing. We experiment with various impact parameters that describe microlensing curves to determine the effectiveness and uncertainty caused by Compressive Sensing. Finally, we describe implications for space-flight missions.

Through-the-Wall Imaging is an ever-expanding area in which processing time, scanning time, vertical, and horizontal resolutions have been tried to improve. In this study, several methods are investigated to obtain efficient reconstruction of through-the-wall imaging radar signals with high resolution. Microwave radar signals, which are produced in YTU Microwave Laboratory, are processed by compressive sensing (CS). B and C scanned reflection data samples collected between 1 and 7 GHz frequency band are taken randomly at 1/4, 1/2 of whole amount and reconstructed by CS method. Considering the signal structure, 10 and 20 compressible Fourier coefficients are taken through CS to analyze the difference between them. In addition, we applied synthetic aperture radar (SAR) processing, also combined with SAR-Multiple Signal Classification over raw data. Experimental performance results are given and shown in the figures with high quality.

Analysis ℓ1-recovery refers to a technique of recovering a signal that is sparse in some transform domain from incomplete corrupted measurements. This includes total variation minimization as an important special case when the transform domain is generated by a difference operator. In the present paper, we provide a bound on the number of Gaussian measurements required for successful recovery for total variation and for the case that the analysis operator is a frame. The bounds are particularly suitable when the sparsity of the analysis representation of the signal is not very small.