Compressive sensing has become an accepted and powerful alternative to conventional data sampling schemes. Hardware simplicity, data, and measurement time reduction and simplified imagery are some of its most attractive strengths. This work aims at exploring the possibilities of using sparse vector recovery theory for actual engineering and defense and securityoriented applications. Conventional throughthewall imaging using a synthetic aperture configuration can also take advantage of compressive sensing by reducing data acquisition rates and omitting certain azimuth scanning positions. An ultrawideband stepped frequency system carrying wide beam antennas performs throughthewall imaging of a real scene, including a hollow concrete block wall and a corner reflector behind it. Random downsampling rates lower than those announced by Nyquist’s theorem both in the fasttime and azimuth domains are studied, as well as downsampling limitations for accurate imaging. Separate dictionaries are considered and modeled depending on the objects to be reconstructed: walls or point targets. Results show that an easy interpretation of throughthewall scenes using the
Previous research studies have explored numerous applications of throughthewall imaging (TWI) in domains which can exploit the convenient penetration capabilities of the 1–5 GHz frequency band in most nonmetal building construction materials [
Synthetic Aperture Radar (SAR) allows competitive TWI using rather common antennas with wide beams and simple outoffocus data acquisition. Thanks to coherent signal integration along a known measurement path, these data are focused on postprocessing, yielding an improved lateral resolution which remains constant at all ranges [
Compressive Sensing (CS) introduces the possibility of reducing the amount of sensed signals for further digital reconstruction and, likewise, to perform accurate TWI. First used to solve sparse vector recovery problems within mathematical applications, CS has been recently used in a growing list of fields for sparse signal reconstruction, including TWI applications [
Actual TWI experiments were conducted for this study. Hollow concrete stretcher blocks were used to build up a solid wall, replicating loadbearing foundation walls used in most permanent constructions. A corner reflector, serving as an object of interest, was placed behind the wall. Scene reconstruction using an ultrawideband moving sensor was achieved, both in conventional SAR and CS approaches. This study will explore the possibilities of random sampling, with a focus on minimizing the amount of data required to produce accurate enough reconstructions of simple TWI scenes. This action will lead to a significant simplification in hardware, as well as reducing processing complexity and data handling. The remaining of this document is divided into four further sections: Section
The sensor used for the presented TWI comprises two Schwarzbeck BBHA 9120 D horn antennas [
Schematic representation of the proposed experimental setup.
Hollow concrete stretcher blocks were used (see Figure
Dimensions of a hollow concrete stretcher block are 385 mm × 185 mm × 135 mm (length, height, and width, resp.). The outer structure is 35 mm thick.
Range estimation is greatly affected by the change of relative permittivity occurring in the airmaterial interfaces. Consequently, imaged targets and walls will appear further away and wider than in reality. Given a material with relative permittivity
The ranging information is altered due to the different transmission media in the wall. Objects will appear further away.
The SAR scanner operated in this study is based on an SF ultrawideband sensor in the 1–5 GHz band. Using such SF sensor guarantees low hardware requirements, since the instantaneous bandwidth is kept narrow, while achieving a remarkable range resolution and power output. Instead of transmitting a linear frequency modulated chirp using a continuous or pulsed approach, the SF sensor produces signals by sequentially generating
Waveform generation scheme of an SF sensor.
For any SF systems, the maximum unambiguous range and range resolution parameters are respectively obtained as follows:
In Table
Descriptive parameters of the TWI experiment.
VNA model  Anritsu 37169A 
Start frequency  1 GHz 
End frequency  5 GHz 

101 
Averaging  10 
Antenna opening angle  14° 

3750 mm 

40 MHz 

4 GHz 
Tx power  +10 dBm 
Tx/RX antennas  Schwarzbeck BBHA 9120 D 
Typ. ant. gain  11 dBi 
Scene size  1500 mm 

37.5 mm 
The signal model of the transmitted waveform
SAR measurements use relatively simple antennas with a small aperture length and, therefore, poor azimuth resolution. By translating the sensor as shown in Figure
Experimental scene description. The SAR sensor moves in azimuth illuminating the scene with a widebeam antenna.
Collected unfocused SAR data must be combined coherently using an SAR focusing algorithm. These algorithms perform range/azimuth compression in order to compact received energy, whether in the time or frequency domains, and are mostly based on the matched filter [
Expected results after an SAR measurement. Energy is spread in azimuth following a hyperbolic function. Certain elements will be shifted in range (dashed lines).
The distance between the sensor’s positions along the azimuth measurement track and any point in the scene is computed using the Euclidean distance and will follow a hyperbolic function. The collected energy from any given point target will present such hyperbolic shape and an amplitude variation in function of the antenna radiation diagram (both transmitting and receiving antennas).
Produced SAR images achieve interesting improved azimuth resolutions, which can be theoretically computed as
In signal acquisition and processing, the NyquistShannon theorem [
Data recovery of sparse vectors is extensively described in the literature [
In radar imaging, vector
Let then
For the application proposed in this study, only the scene reflectivity coefficients in
Optimization of noisy measurements must be approximated since a perfect reconstruction will not be possible [
Several categories different from convex optimization or basis pursuit can be found, each one offering multiple algorithms and variations. One of the most popular in terms of simplicity and efficiency is Orthogonal Matching Pursuit (OMP) [
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and update residual with
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Random downsampling in the fasttime and azimuth dimensions implies a substantial reduction in data collection, in measurement time (less azimuth scans), and sensor complexity (fasttime sampling is less demanding). Random sampling schemes must be cautiously imitated when constructing the CS dictionary
Sample selection scheme on full SAR data simulating a real CS sensor. Fasttime samples in white and azimuth measurements in grey are skipped.
CS dictionaries can be modeled according to the type of scene that must be reconstructed. A possible solution for the problem here addressed is considering two regions in the measurement (Figure
A region closer to the sensor (wall region) where only walls parallel to the sensors’ motion path are expected to appear. Since walls present very strong azimuth redundancies in SAR measurements, the wall region can be reconstructed forcing coarse azimuth and range resolutions in the final imagery. For every possible range in the scene, the wall dictionary will contain in its columns simulated received SAR data based on a simple infinite wall model (Figure
A second region is defined further away from the sensor, where scatterers other than walls are expected. This region is known as the wallfree region. Sufficient azimuth information is necessary to characterize point targets in the scene, and reducing the number of azimuth positions is not a sound option. For each position of a point target in the scene, received SAR signals are simulated and included in the columns of the pointtarget dictionary (Figure
Two regions are described and will be treated differently. Walls may appear closer to the sensor. Further away only point targets are expected.
Rangecompressed images of a simulated stepped frequency SAR system. (a) a scene containing scatterers modeling a simple wall model located at 0.99 m in range, used to populate the wall dictionary. (b) a scene containing onesingle point target located at range 1.9 m and azimuth 0.75 m, used to populate the pointtarget dictionary.
Estimating the number of required random samples for CS reconstruction is a complex task since scene sparsity cannot be easily assessed prior to the measurement. However, an approximate expertise can be gained by systematically testing out several random downsampling possibilities. As discussed in Section
PSNR values in dB for different random downsampling possibilities in fast time and azimuth. A timedomain signal model was used to create the dictionary.
Given the presented results, this study will use a random downsampling of 50% of the usual samples for both fasttime and azimuth dimensions in the wallfree region, which implies keeping only 25% of the necessary samples for conventional SAR processing. Additionally, decimation by two of the azimuth measurements can be safely applied for the wall region, yielding 12.5% of the original data.
The experimental TWI setup uses a conventional SAR system, and original CS measurements cannot be obtained. A full SAR measurement is performed with the presented SF SAR system in order to obtain sufficient fasttime and azimuth information for further random downsampling. The SAR simulator used to model the expected scatterers operates likewise.
The experimental setup depicted in Figures
(a) A rangecompressed SAR image. The wall is clearly seen. (b) The energy of the corner reflector is spread in azimuth at approximate range 2.25 m. (c) A fully processed SAR image where the presence of a corner reflector is clearly spotted at range 2.25 m.
After having taken into account azimuth information, the fully compressed SAR image is reconstructed as shown in Figure
A CS head and processor are imitated in software following the considerations explained in Sections
Figure
Block diagrams of the (a) wall and pointtarget dictionary generation and (b) scene reconstruction from actual incomplete measurements.
Figure
CS reconstruction of the scene using a coarse wall dictionary for wall ranging. The actual wall was located at 0.95 m.
A more accurate CS dictionary is then used for pointtarget reflectivity coefficients reconstruction, or vector
CS reconstructions of the behindthewall scene using a pointtarget dictionary. Downsampling factors were set to 60% for fasttime and 50% for azimuth. (a)
CS reconstructions of the behindthewall scene using a pointtarget dictionary. Downsampling factors were set to 50% for fasttime and 50% for azimuth. (a)
CS reconstructions of the behindthewall scene using a pointtarget dictionary. Downsampling factors were set to 40% for fasttime and 50% for azimuth. (a)
Figure
In this work, CS has been successfully applied to TWI of a real concrete wall. SAR measurements were preprocessed in software to simulate a CS sensor which would perform random sampling in the fasttime and azimuth dimensions. The particular considerations regarding the application of CS onto SAR measurements for TWI were addressed. By using CS, any kind of SAR processing was avoided. A conceptually simple procedure was designed to automatically distinguish between wall and wallfree regions, which exploits the possibilities that CS can offer and reduces computational complexity and avoids having to treat wall clutter. A systematic investigation was performed to determine the minimum random downsampling with respect to conventional SAR TWI without compromising reconstruction accuracy. Data volume was reduced to as low as 25% of the usual required samples, enabling measurement time and hardware complexity reduction.
Future work is focused on finding alternatives to further exploit the CS capabilities for TWI. Some of the lines of investigation the authors are following related to signal processing and CS are as follows.
Reducing the effects of strong reflections from the wall introduces the reconstruction of pointtarget regions and improves the accuracy of detection. The authors currently are working on strategies to overcome these negative effects.
Multiple echoes and patterns due to the wall structure appear in further adjacent ranges. Using a complete SAR model of a wall will help identify which scatterers can be considered as wall clutter or targets of interest behind the wall.
Range inaccuracies due to inhomogeneous transmission media will be corrected to provide a correct range estimation. A complete wall model will be developed based on existing publications.
The SF system used in the experiments as well as the antennas has a frequencydependent performance. A complete SAR signal model must be developed to create CS dictionaries as accurate as possible. Moreover, the mutual interaction between both adjacent antennas modifies their radiation patterns. The antennas will be measured in an anechoic chamber to include this effect in the complete signal model.
CS applied to 3D SAR imaging proposes challenging open questions regarding sparsity assessment and strategies to guarantee the viability the of proposed methodologies in this work.
Data transformation bases will be studied to enhance data sparsity and facilitate accurate scene reconstructions with even less random samples and simpler hardware.
Other efficient sparse data reconstruction algorithms will be explored and modified to the TWI needs where applicable.
The authors of this study would like to show their gratitude to the OMRA and LEMA laboratories of the Royal Military Academy, Belgium, for providing both technical support and logistic support during construction and measurement of the presented experimental scenes.