Ali Cafer Gurbuz

A Compressive Sensing Data Acquisition and Imaging Method for Stepped Frequency GPRs

A novel data acquisition and imaging method is presented for stepped-frequency continuous-wave ground penetrating radars (SFCW GPRs). It is shown that if the target space is sparse, i.e., a small number of point like targets, it is enough to make measurements at only a small number of random frequencies to construct an image of the target space by solving a convex optimization problem which enforces sparsity through lscr 1 minimization. This measurement strategy greatly reduces the data acquisition time at the expense of higher computational costs. Imaging results for both simulated and experimental GPR data exhibit less clutter than the standard migration methods and are robust to noise and random spatial sampling. The images also have increased resolution where closely spaced targets that cannot be resolved by the standard migration methods can be resolved by the proposed method.

A compressive beamforming method

Compressive sensing (CS) is an emerging area which uses a relatively small number of non-traditional samples in the form of randomized projections to reconstruct sparse or compressible signals. This paper considers the direction-of-arrival (DOA) estimation problem with an array of sensors using CS. We show that by using random projections of the sensor data, along with a full waveform recording on one reference sensor, a sparse angle space scenario can be reconstructed, giving the number of sources and their DOAs. The number of projections can be very small, proportional to the number sources. We provide simulations to demonstrate the performance and the advantages of our compressive beamformer algorithm.

Multistatic Ground-Penetrating Radar Experiments

A multistatic ground-penetrating radar (GPR) system has been developed and used to measure the response of a number of targets to produce data for the investigation of multistatic inversion algorithms. The system consists of a linear array of resistive-vee antennas, microwave switches, a vector network analyzer, and a 3-D positioner, all under computer control. The array has two transmitters and four receivers which provide eight bistatic spacings from 12 to 96 cm in 12-cm increments. Buried targets are scanned with and without surface clutter, which is a layer of rocks whose spacing is empirically chosen to maximize the clutter effect. The measured responses are calibrated so that the direct coupling in the system is removed, and the signal reference point is located at the antenna drive point. Images are formed using a frequency-domain beamforming algorithm that compensates for the phase response of the antennas. Images of targets in air validate the system calibration and the imaging algorithm. Bistatic and multistatic images for the buried targets are very good, and they show the effectiveness of the system and processing.

Analysis of Energy Efficiency of Compressive Sensing in Wireless Sensor Networks

Improving the lifetime of wireless sensor networks (WSNs) is directly related to the energy efficiency of computation and communication operations in the sensor nodes. Compressive sensing (CS) theory suggests a new way of sensing the signal with a much lower number of linear measurements as compared to the conventional case provided that the underlying signal is sparse. This result has implications on WSN energy efficiency and prolonging network lifetime. In this paper, the effects of acquiring, processing, and communicating CS-based measurements on WSN lifetime are analyzed in comparison to conventional approaches. Energy dissipation models for both CS and conventional approaches are built and used to construct a mixed integer programming framework that jointly captures the energy costs for computation and communication for both CS and conventional approaches. Numerical analysis is performed by systematically sampling the parameter space (i.e., sparsity levels, network radius, and number of nodes). Our results show that CS prolongs network lifetime for sparse signals and is more advantageous for WSNs with a smaller coverage area.

Compressive Sensing for GPR Imaging

The theory of compressive sensing (CS) enables the reconstruction of sparse signals from a small set of non-adaptive linear measurements by solving a convex lscr1 minimization problem. This paper presents a novel data acquisition and imaging algorithm for ground penetrating radars (GPR) based on CS by exploiting sparseness in the target space, i.e., a small number of point-like targets. Instead of measuring conventional radar returns and sampling at the Nyquist rate, linear projections of the returned signal with random vectors are taken as measurements. Using simulated and experimental GPR data, it is shown that sparser and sharper target space images can be obtained compared to standard backprojection methods using only a small number of CS measurements. Furthermore, the target region can even be sampled at random aperture points.

Compressive wireless arrays for bearing estimation

Joint processing of sensor array outputs improves the performance of parameter estimation and hypothesis testing problems beyond the sum of the individual sensor processing results. When the sensors have high data sampling rates, arrays are tethered, creating a disadvantage for their deployment and also limiting their aperture size. In this paper, we develop the signal processing algorithms for randomly deployable wireless sensor arrays that are severely constrained in communication bandwidth. We focus on the acoustic bearing estimation problem and show that when the target bearings are modeled as a sparse vector in the angle space, low dimensional random projections of the microphone signals can be used to determine multiple source bearings by solving an l 1-norm minimization problem. Field data results are shown where only 10 bits of information is passed from each microphone to estimate multiple target bearings.

Bearing Estimation via Spatial Sparsity using Compressive Sensing

Bearing estimation algorithms obtain only a small number of direction of arrivals (DOAs) within the entire angle domain, when the sources are spatially sparse. Hence, we propose a method to specifically exploit this spatial sparsity property. The method uses a very small number of measurements in the form of random projections of the sensor data along with one full waveform recording at one of the sensors. A basis pursuit strategy is used to formulate the problem by representing the measurements in an over complete dictionary. Sparsity is enforced by ℓ1-norm minimization which leads to a convex optimization problem that can be efficiently solved with a linear program. This formulation is very effective for decreasing communication loads in multi sensor systems. The algorithm provides increased bearing resolution and is applicable for both narrowband and wideband signals. Sensors positions must be known, but the array shape can be arbitrary. Simulations and field data results are provided to demonstrate the performance and advantages of the proposed method.

Ground Reflection Removal in Compressive Sensing Ground Penetrating Radars

Recent results in compressive sensing (CS)-based subsurface imaging showed that, if the target space is sparse, it can be reconstructed with many fewer number of measurements from a stepped frequency ground penetrating radar (GPR). One of the problems in this CS subsurface imaging is the surface reflections. Previous work dealed with surface reflections using a model dictionary generated from the target space excluding specifically the near surface region. While this works fine for some applications, it might lack the imaging of near surface targets. Removing the surface reflections with standard methods is not directly applicable since only very few and random measurements in the frequency domain are taken. This letter provides a simple surface reflection method using compressive measurements, that can be used for nonplanar surfaces. It is observed in both simulated and experimental GPR data that the CS-based imaging method is more robust and can find shallow targets using the surface-reflection-removed data.

Perturbed Orthogonal Matching Pursuit

Compressive Sensing theory details how a sparsely represented signal in a known basis can be reconstructed with an underdetermined linear measurement model. However, in reality there is a mismatch between the assumed and the actual bases due to factors such as discretization of the parameter space defining basis components, sampling jitter in A/D conversion, and model errors. Due to this mismatch, a signal may not be sparse in the assumed basis, which causes significant performance degradation in sparse reconstruction algorithms. To eliminate the mismatch problem, this paper presents a novel perturbed orthogonal matching pursuit (POMP) algorithm that performs controlled perturbation of selected support vectors to decrease the orthogonal residual at each iteration. Based on detailed mathematical analysis, conditions for successful reconstruction are derived. Simulations show that robust results with much smaller reconstruction errors in the case of perturbed bases can be obtained as compared to standard sparse reconstruction techniques.

Knowledge Exploitation for Human Micro-Doppler Classification

Micro-Doppler radar signatures have great potential for classifying pedestrians and animals, as well as their motion pattern, in a variety of surveillance applications. Due to the many degrees of freedom involved, real data need to be complemented with accurate simulated radar data to be able to successfully design and test radar signal processing algorithms. In many cases, the ability to collect real data is limited by monetary and practical considerations, whereas in a simulated environment, any desired scenario may be generated. Motion capture (MOCAP) has been used in several works to simulate the human micro-Doppler signature measured by radar; however, validation of the approach has only been done based on visual comparisons of micro-Doppler signatures. This work validates and, more importantly, extends the exploitation of MOCAP data not just to simulate micro-Doppler signatures but also to use the simulated signatures as a source of a priori knowledge to improve the classification performance of real radar data, particularly in the case when the total amount of data is small.