Performance Analysis of Compressive-Sensing-Based Through-the-Wall Imaging with Effect of Unknown Parameters

Compressive Sensing (CS) is a very useful algorithm that is used in Ground Penetrating Radar (GPR) or through the wall imaging (TWI). CS generates high resolution images by decreasing the required measurement number. Although there are several recent studies about TWI with CS, they assume that targets are point like positioned at only discrete grid locations and wall thickness and its dielectric constant are perfectly is known. However, in real applications, it is not possible to know the exact target positions or estimate the wall parameters definitely. This work details the theory for CS based TWI and analyzes the imaging ability of CS. In addition, in this work, the effect of errors in unknown parameters on the imaging performance is analyzed and possible solutions are discussed.

Recently, compressed sensing (CS) has been widely used in ground penetrating radar (GPR) imaging due to its low sampling time, high quality performance and high quality underground imaging results. There are always a large number of matrix operations involved in CS based GPR imaging process, which takes a long time. Traditionally, all scanning area was imaged by this CS imaging method. However, with the imaging scene becoming larger, the measurement matrix and the data dictionary in CS imaging model expand, which increases the time of CS-based imaging process. Thus, this paper proposes a fast CS based GPR imaging method to reduce the imaging time. Specifically, the geometric characteristics of the B-scan image can firstly be used to extract the region of interest (ROI) where the target may exist in a layered medium. Then the GPR imaging based on CS can be realized in ROI, which can reduce the imaging area and imaging time. Experimental results present that the method can effectively reduce the time of GPR imaging based on CS.

In most scenes of through-the-wall imaging (TWI), the observation zone is spares. So the radar signals could be processed using Compressive Sensing (CS) technique. Existing greedy algorithms for CS, such as orthogonal Matching Pursuit (OMP) algorithm and Compressive Sampling Matching pursuit (CoSaMP), suffer from artifacts and low resolution respectively. To cover the shortage of existing algorithms, a modified Compressive Sampling Matching Pursuit algorithm is proposed. By using the orthogonality among selected basis-signals and backtracking strategy for basis-signals reevaluation, the proposed algorithm could reconstruct radar signal. Then the image of observation zone could be got using Delay and Sum (DAS) beamforming method. Measurement results demonstrate the effectiveness of the proposed algorithm.

This paper presents a new ground penetrating radar (GPR) design approach using orthogonal frequency division multiplexing (OFDM) and compressive sensing (CS) algorithms. OFDM technique is applied to leverage GPR operating speed with multiple frequency tones transmission and receiving concurrently, and CS technique allows utilizing reduced frequency tones without compromising data reconstruction accuracy. Combination of OFDM and CS boosts the radar operating efficiency. For GPR image reconstruction, a synthetic aperture radar (SAR) technique is implemented.

Through-the-wall imaging (TWI) is a challenging problem, even if the wall parameters and characteristics are known to the system operator. Proper target classification and correct imaging interpretation require the application of high resolution techniques using limited array size. In inverse synthetic aperture radar (ISAR), signal subspace methods such as Multiple Signal Classification (MUSIC) are used to obtain high resolution imaging. In this paper, we adopt signal subspace methods and apply them to the 2-D spectrum obtained from the delay-andsum beamforming image. This is in contrast to ISAR, where raw data, in frequency and angle, is directly used to form the estimate of the covariance matrix and array response vector. Using beams rather than raw data has two main advantages, namely, it improves the signal-to-noise ratio (SNR) and can correctly image typical indoor extended targets, such as tables and cabinets, as well as point targets. The paper presents both simulated and experimental results using synthesized and real data. It compares the performance of beam-space MUSIC and Capon beamformer. The experimental data is collected at the test facility in the Radar Imaging Laboratory, Villanova University.

Recently, compressed sensing (CS) has been widely used in ground penetrating radar (GPR) imaging due to its low sampling tune, high quality performance and high quality imaging results in underground imaging. However, for densely distributed underground multi-target, the error of GPR imaging based on CS is large. So, this paper proposes a filter matrix, which can effectively reduce the energy of B-scan hyperbolic arms, increase the hyperbolic apex energy, and reduce the error of GPR imaging based on CS in densely distributed multi-target environment. The algorithm also takes into account the distance between the antenna and the ground. At first, a method of the normalized is used to calculate the echo data. Then the filter matrix designed in this paper is used. Experimental results present that the filter matrix can effectively reduce the imaging error in multi-target environment.

Ground penetrating radar (GPR) is a non-destructive and continuous electromagnetic (EM) detection technique for civil and environmental parameter measurement applications such as pavement condition and soil property characterization. This technique is based on the measurement of the travel time and reflection amplitude of a short EM pulse, which are functions of medium properties. Most GPR measurements of sub-layer thickness are conducted based on the priori knowledge of dielectric constants of the pavement materials. And actually, the dielectric constant is an unknown but important parameter in the applications. For some applications, the dielectric constants are estimated based on manuals or tables that can only provide rough results not the real changes of pavement materials. In some other cases, the dielectric constants are estimated by using the surface reflectivity information. However, such method is not applicable for rough surface and ground-coupled GPR applications. Compared to the air-launching GPR mode, the ground-coupled mode is more complicated because of the coupling effect between the antennas and ground. In this paper, numerical simulations about the wave propagation paths of the ground-coupled GPR are conducted. The simulation results reveal some interesting ray paths of GPRs in the ground-coupled mode. And based on the simulation results, new methods are introduced for calculating the pavement dielectric constant and thickness directly from the ground-coupled GPR data. Finally, applications and field test results for pavement evaluation are presented.

BackgroundHigh-dimensional proteomics data present significant challenges in biomarker discovery due to technical noise, feature redundancy, and multicollinearity. Current feature selection methods, including filter, wrapper, and embedded approaches, struggle with stability, sparsity, and computational efficiency. To address these limitations, we propose Soft-Thresholded Compressed Sensing (ST-CS), a hybrid framework integrating 1-bit compressed sensing with K-Medoids clustering. Unlike conventional methods relying on manual thresholds, ST-CS automates feature selection by dynamically partitioning coefficient magnitudes into discriminative biomarkers and noise.ResultsEvaluations on simulated and real-world proteomic datasets demonstrated ST-CS’s superiority in feature selection capability and classification performance. In simulations, ST-CS achieved feature selection robustness with balanced sensitivity (> 80%) and specificity (> 99.8%), reducing false discovery rates (FDR) by 20–50% compared to Hard-Thresholded Compressed Sensing (HT-CS). Additionally, it attained superior F1 scores and Matthews Correlation Coefficients (MCC), outperforming HT-CS, LASSO, and SPLSDA in identifying true biomarkers while suppressing noise. For classification performance, ST-CS surpassed all methods in the area under the receiver operating characteristic curve (AUC) across varying noise levels while maintaining sparsity. Applied to Clinical Proteomic Tumor Analysis Consortium (CPTAC) datasets, ST-CS matched HT-CS’s classification accuracy (AUC = 97.47% for intrahepatic cholangiocarcinoma) but with 57% fewer selected features (37 vs. 86), demonstrating its dual strength in precision biomarker discovery and predictive accuracy. For glioblastoma data, ST-CS achieved higher AUC (72.71%) than HT-CS (72.15%), LASSO (67.80%), and SPLSDA (71.38%) while retaining a parsimonious feature set (30 vs. 58 features for HT-CS). In ovarian serous cystadenocarcinoma, ST-CS further demonstrated its adaptability, attaining superior AUC (75.86%) over HT-CS (75.61%), LASSO (61.00%), and SPLSDA (70.75%) with only 24 ± 5 selected biomarkers. These results highlight ST-CS’s ability to rigorously automate feature selection while balancing classification efficacy, interpretability, and scalability for translational proteomics.

This study provides a comprehensive analysis of Ground Penetrating Radar (GPR) data processing techniques for detecting water leakage in urban pavements. By examining GPR images characterized by continuous and discontinuous high-amplitude reflections, the research identifies clear indicators of water saturation caused by leaking underground pipes. Computer modeling of GPR profiles enables effective comparisons with real data and helps in calibrating key GPR attributes such as energy, amplitude variance, and RMS amplitude. These attributes allow for the precise delineation of leakage zones in both synthetic and real GPR datasets collected in the Amazon region of Brazil. The Reflector Tilt Method (RTM) significantly enhances GPR data analysis, especially for detecting subsurface water leaks. RTM utilizes changes in the relative dielectric constant and electromagnetic wave velocity induced by water saturation in unconsolidated, horizontally stratified sand layers. By analyzing the tilt of reflections in GPR profiles, RTM differentiates between dry and saturated zones, providing insights into the geometry and extent of water infiltration. Notably, this study demonstrates how increased subsurface water saturation causes underlying reflectors to tilt. Using the tilt angle, we propose a novel technique to quantify the increase in the dielectric constant due to water saturation. This technique could also be adapted to detect leaks involving other fluids, as long as there is a strong contrast between the dielectric constant and the background. The integration of RTM improves the creation of accurate three-dimensional models of affected areas, enhancing leak detection and aiding in understanding water movement dynamics within the subsurface. The study underscores the importance of combining GPR attributes with RTM to generate detailed 3D models of leakage zones, which are essential for estimating the volume of infiltrated areas. Observations indicate significant water saturation near leaking pipes at shallow depths, with saturation levels decreasing rapidly as depth increases. By identifying 2D geophysical signatures of water leaks in public distribution networks, the research highlights the effectiveness of non-invasive GPR methods in mitigating risks such as soil erosion and surface collapse. This approach demonstrates the utility of GPR attributes and RTM as essential tools for assessing urban pavement integrity, enabling early detection of leaks and precise mapping of affected zones. The findings contribute significantly to the efficient and sustainable management of urban infrastructure, enhancing maintenance strategies and reducing potential hazards associated with undetected fluid leaks.

Location-Based Services have become an indispensable part of our daily life, the sparsity of location finding makes it possible to estimate specific position by Compressive Sensing (CS). Using public Frequency Modulation (FM) broadcasting and Digital Television Terrestrial Multimedia Broadcasting (DTMB) signals, this paper presents an indoor positioning scheme, which is consisted of an offline stage and an online stage. In the offline stage, the Received Signal Strength (RSS) at the Reference Points (RPs) is measured, including the average and variance of public FM broadcasting and DTMB signals. In the online stage, the K-Weighted Nearest Neighbor algorithm is used to fulfill coarse positioning, which is able to narrow the selection scope of locations and choose partial RPs for accurate positioning. Then, the accurate positioning is implemented through CS. Experiment shows that the average positioning error of the proposed scheme is 1.63m. What's more, a CS-based method has been proposed in this paper to reduce the labor cost when collecting data. Experiment shows the average positioning error is 2.04m, with the advantage of a 34% labor cost reduction. Experiment results indicate that the proposed system is a practical indoor positioning scheme.

Compressive sensing (CS)-based data gathering is a promising method to reduce energy consumption in wireless sensor networks (WSNs). Traditional CS-based data-gathering approaches require a large number of sensor nodes to participate in each CS measurement task, resulting in high energy consumption, and do not guarantee load balance. In this paper, we propose a sparser analysis that depends on modified diffusion wavelets, which exploit sensor readings’ spatial correlation in WSNs. In particular, a novel data-gathering scheme with joint routing and CS is presented. A modified ant colony algorithm is adopted, where next hop node selection takes a node’s residual energy and path length into consideration simultaneously. Moreover, in order to speed up the coverage rate and avoid the local optimal of the algorithm, an improved pheromone impact factor is put forward. More importantly, theoretical proof is given that the equivalent sensing matrix generated can satisfy the restricted isometric property (RIP). The simulation results demonstrate that the modified diffusion wavelets’ sparsity affects the sensor signal and has better reconstruction performance than DFT. Furthermore, our data gathering with joint routing and CS can dramatically reduce the energy consumption of WSNs, balance the load, and prolong the network lifetime in comparison to state-of-the-art CS-based methods.

The chapter focuses on minimizing the amount of wireless transmission in sensory data gathering for correlated data field monitoring in wireless sensor networks (WSN), which is a major source of power consumption. Compressive sensing (CS) is a new in-node compression technique that is economically used for data gathering in an energy-constrained WSN. Among existing CS-based routing, cluster-based methods offer the most transmission-efficient architecture. Most CS-based clustering methods randomly choose nodes to form clusters, neglecting the topology structure. A novel base station (BS)-assisted cluster, spatially correlated cluster using compressive sensing (SCC_CS), is proposed to reduce number of transmissions in and form the cluster by exploiting spatial correlation based on geographical proximity. The proposed BS-assisted clustering scheme follows hexagonal deployment strategy. In SCC_CS, cluster heads are solely involved in data gathering and transmitting CS measurements to BS, saving intra-cluster communication cost, and thus, network life increases as proved by simulation.

Recently, Compressive Sensing (CS) has been applied to array signal processing. In theory, Direction-of-Arrival (DOA) estimation based on CS recovery can work well in correlated environments. However, a large number of sensors (i.e., linear measurements) are still needed for CS recovery. To improve on this, we propose a new CS-based DOA estimation method with a recently designed antenna structure called the Asymmetric Antenna without Phase Center (Asym-AWPC). The best reconstruction is achieved by solving the l1-norm optimization problem, which is cast as an l1-regularized least-squares program. Simulated results indicate the effectiveness of the proposed CS-based Asym-AWPC DOA estimator in a multipath environment over a recent Asym-AWPC DOA estimator but using the Multiple Signal Classification (MUSIC) rather than CS. Further improvement on the resolution can be achieved by tuning the degree of asymmetry in designing the Asym-AWPC.

Ground penetrating radar (GPR) is one of the most commonly used technologies for non-destructive testing (NDT). With the development of GPR signal processing methodologies, researchers are becoming more concerned not just with the detection of the target itself, but also with their physical properties and main features. In general, full waveform inversion algorithm is required to achieve this aim. But, full waveform inversion problem is a costive approach which need a huge computation. Thus, the ultimate goal of this study is to explore an effective strategy for estimating the relative permittivity of the target using polarimetric GPR data. We have investigated the relation between relative permittivity and polarimetric alpha angle based on the data collected by dualpolarization antennas GPR system. Laboratory experiments that measures different moisture sand targets (simulating for different relative permittivity target) in tree trunk holes have been carried out, taken as analog models for the physiological process representing decays in trees. After signal processing, the rough results that alpha angle versus with relative permittivity were obtained. The results show that for a dry sand the polarimetric alpha angle is small and the polarimetric alpha angle increases with increasing water content.

<p>As a recognised non-destructive testing (NDT) tool, Ground Penetrating Radar (GPR) is becoming increasingly common in the field of environmental engineering [1]-[3]. GPR uses electromagnetic (EM) waves which travel at specific velocity determined by the permittivity of the material. With the development of new GPR signal processing methodologies, finding information on the physical properties of hidden targets has become a key target. Currently, only three types of approach could be applied for the quantitative estimation of permittivity from GPR data, i.e., hyperbola curve fitting, common middle point (CMP) velocity analysis and full-waveform inversion. However, the main challenges for the estimation of permittivity from GPR backscattered signals are to provide effective and accurate strategy for prediction.</p><p>In this research, we used a dual-polarimetric GPR system to estimate the dielectric constant of targets. The system is equipped with two 2GHz antennas polarised perpendicularly each to one another (HH and VV). The dual polarisation enables deeper surveying, providing images of both shallow and deeper subsurface features. Polarimetry is a property of EM waves that generally refers to the orientation of the electric field vector, which plays here an important role as it allows either direct or parameterisation permittivity effects within the scattering problem in the remote sensing [4].</p><p>The aim of this research is to provide a novel and more robust approach for dielectric constant prediction using a dual-polarimetric GPR system. To this extent, the relationship between the relative permittivity and the polarimetric alpha angle have been investigated based on data collected by a GPR system with dual-polarised antennas. The approach was then assessed by laboratory experiments where different moisture sand targets (simulating the effect of different relative permittivity targets) were measured. After signal processing, a clear relationship between the alpha angle and the relative permittivity was obtained, proving the viability of the proposed method.</p><p> </p><p><strong>Acknowledgements</strong></p><p>The authors would like to express their sincere thanks and gratitude to the following trusts, charities, organisations and individuals for their generosity in supporting this project: Lord Faringdon Charitable Trust, The Schroder Foundation, Cazenove Charitable Trust, Ernest Cook Trust, Sir Henry Keswick, Ian Bond, P. F. Charitable Trust, Prospect Investment Management Limited, The Adrian Swire Charitable Trust, The John Swire 1989 Charitable Trust, The Sackler Trust, The Tanlaw Foundation, and The Wyfold Charitable Trust.</p><p> </p><p><strong>References</strong></p><p>[1] Zou, L. et al., 2020. Mapping and Assessment of Tree Roots using Ground Penetrating Radar with Low-Cost GPS. Remote Sensing, vol.12, no.8, pp:1300.</p><p>[2] Zou, L. et al., 2020. On the Use of Lateral Wave for the Interlayer Debonding Detecting in an Asphalt Airport Pavement Using a Multistatic GPR System. IEEE Transactions on Geoscience and Remote Sensing, vol. 58, no. 6, pp. 4215-4224.</p><p>[3] Zou, L. et al., 2021. Study on Wavelet Entropy for Airport Pavement Debonded Layer Inspection by using a Multi-Static GPR System. Geophysics, vol. 86, no. 3, pp. WB69-WB78.</p><p>[4] J. Lee and E. Pottier, Polarimetric Imaging: From Basics to Applications, FL, Boca Raton: CRC Press, 2009.</p>