research article cylindrical three-dimensional millimeter-wave imaging...

Research ArticleCylindrical Three-Dimensional Millimeter-Wave Imaging viaCompressive Sensing

Guoqiang Zhao Shiyong Li Bailing Ren Qingwei Qiu and Houjun Sun

Beijing Key Laboratory of Millimeter Wave and Terahertz Technology Beijing Institute of Technology Beijing 100081 China

Correspondence should be addressed to Shiyong Li lisy 98biteducn

Received 31 December 2014 Revised 16 July 2015 Accepted 28 July 2015

Academic Editor Ali Yapar

Copyright copy 2015 Guoqiang Zhao et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Millimeter-wave (MMW) imaging techniques have been used for the detection of concealed weapons and contraband carried bypersonnel However the future application of the new technology may be limited by its large number of antennas In order toreduce the complexity of the hardware a novel MMW imaging method based on compressive sensing (CS) is proposed in thispaper The MMW images can be reconstructed from the significantly undersampled backscattered data via the CS approach Thusthe number of antennas and the cost of system can be further reduced than those based on the traditional imaging methods thatobey the Nyquist sampling theorem The effectiveness of the proposed method is validated by numerical simulations as well as byreal measured data of objects

1 Introduction

Millimeter-wave (MMW) imaging techniques have beenapplied for the detection of concealed weapons and con-traband carried by personnel at airports and other securelocations [1ndash5] Millimeter waves can penetrate commonclothing barriers to form an image of a person as well asany concealed items with different reflectivity or emissivityAlso millimeter waves are nonionizing and therefore poseno known health hazard at moderate power levels not likeX-ray systems

However a largenumberof antennas and switches (maybefrom hundreds to ten thousands) are needed to constructone- or two-dimensional (1D or 2D) array to obtain three-dimensional (3D) images which increases the cost of theimaging system and then limits its wide application In orderto reduce the complexity and cost of the system we proposea compressive sensing- (CS-) based method for 3D MMWimaging The area of CS was initiated in 2006 by Candes etal [6] and by Donoho [7]

CS has been widely explored in the domain of radarimaging [8ndash11] in which the image was usually converted

into a vector And the 1D optimization algorithm was usedto recover the image However if we convert the 3D imageinto a vector a huge sensing matrix will be introduced Thenthe computational complexity will be largely increased Inthis paper we introduce an operator as the sensing matrix torepresent the traditional imaging process based onwavenum-ber domain algorithm (WDA) [12] Thus large-scale matrixcomputations are avoidedThe image resolution of the WDAis determined by signal bandwidth signal frequency and thelength of synthetic aperture And the resolution of the CS-based imaging algorithm is determined mainly by the signal-to-noise ratio and the matching degree of signal model to therequirements of CS such as the restricted isometry property(RIP) The simulation and experiment results show that theCS-based method offers a much more accurate image thanthe traditional WDA just using a small subset of the fullsamples

The rest of the paper is organized as follows In Section 2the CS imaging method based on the traditional WDA isintroduced The results demonstrating the efficiency andaccuracy of the method are shown in Section 3 Section 4summarizes the conclusions

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2015 Article ID 218751 6 pageshttpdxdoiorg1011552015218751

2 International Journal of Antennas and Propagation

O

ElevationAntenna element

Azimuth

x

z

(x y z)

y

O120579998400

(R0 cos120579998400 y998400 R0 sin120579998400)

Figure 1 Cylindrical near-field 3D imaging configuration

Raw data

Elevation FFT

Azimuth IFFT

2D interpolation

3D IFFT

Complex image

Azimuth FFT

Azimuth FFT

divide

exp(jky y9984000)

exp(minusj2krR0)exp[minusj(radic4kr

2 minus ky9984002R0 cos(120579998400))]

Figure 2 Scheme of the wavenumber domain algorithm

2 CS-Based Method for 3D MMW Imaging

For the 3D imaging geometry is illustrated in Figure 1 Anobject formed by a distribution of independent scatterers ofreflectivity 119892(119909 119910 119911) is located at the center of the imagingscene The backscattered field 119884(119896 120579 119910

1015840) after demodulation

is given by

119884 (119896 120579 1199101015840) = ∭

119909119910119911

119892 (119909 119910 119911)

sdot exp [minus11989521198961198771205791199101015840 (119909 119910 119911)] d119909 d119910 d119911

(1)

where 119896 = 2120587119891119888 is the spatial frequency119888 represents the light speed 119877

1205791199101015840(119909 119910 119911) =

radic(1198770 cos 120579 minus 119909)2 + (1198770 sin 120579 minus 119911)2+ (1199101015840 minus 119910)

2 is the distancefrom each antenna element at (1198770 cos 120579 119910

1015840 1198770 sin 120579) to each

scattering center at (119909 119910 119911) and 1198770 is the radius of thecylindrical aperture as shown in Figure 1

The scheme of the traditional WDA [12] for near-fieldcylindrical 3D imaging is illustrated in Figure 2We representthe imaging process as an operator Then the inverse processcan be represented as the inversion of the operator Thus theimaging process is given by

119892 (119909 119910 119911) = 119866 [119884 (119896 120579 1199101015840)] (2)

where the operator 119866 denotes the imaging process as shownin Figure 2 that is

119866 = IFFT3D IN2D IFFT119896120579

FFT120579[FFT1199101015840 (sdot)]

sdot FFT120579exp [119895119896

1199091199111198770 cos (120579)]

(3)

where IN2D(sdot) represents 2D interpolation

International Journal of Antennas and Propagation 3

minus005

0

005 minus0050

005

minus005

0

005

Azimuth-range (m)

Range (m)

Elev

atio

n-ra

nge (

m)

Figure 3 Target model

Then 119884(119896 120579 1199101015840) can be expressed as the inversion of (2)

as follows

119884 (119896 120579 1199101015840) = 119866

minus1[119892 (119909 119910 119911)] (4)

where 119866minus1 denotes the inverse process of (3)

Due to the sparsity of the image scene 119892(119909 119910 119911) only asmall subset of scattered data 119884(119896 120579 119910

1015840) is enough to be used

to reconstruct the image exactly by solving the optimizationproblem [13]

min119892

1003817100381710038171003817120595119892 (119909 119910 119911)10038171003817100381710038170

st 119884 (119896 120579 1199101015840) = 119866

minus1[119892 (119909 119910 119911)]

(5)

where sdot 0 is simply the number of nonzero components of120595119892 and 120595 represents a sparse transform making 120595119892 a sparsevector

However solving (5) is an NP-hard problem and thuspractically not feasible Instead its convex relaxation isusually considered as

min 10038171003817100381710038171003817119884 (119896 120579 119910

1015840) minus119866minus1

[119892 (119909 119910 119911)]10038171003817100381710038171003817

22

+1205821003817100381710038171003817120595119892 (119909 119910 119911)

10038171003817100381710038171

(6)

where sdot 1 and sdot 2 denote the ℓ1 norm and ℓ2 normrespectively In this paper we use the total-variation (TV) as asparse transformThe parameter 120582 is used to balance the twinobjectives of minimizing both error and sparsity

The operators 119866 and 119866minus1 correspond to the Fourier

matrices if we express the signal model directly Thus 119866 and119866minus1 satisfy the RIP required by CS and both (5) and (6)

have the same unique solution [6] There are many state-of-the-art optimization algorithms designed to solve the convexoptimization problem of (6) [14ndash17] Here we use a nonlinearconjugate gradient (CG) descent algorithm described in[18] The computational complexities of 119866minus1[119892(119909 119910 119911)] and119866[119884(119896 120579 119910

1015840)] both are an order of (NMP)sdotlog2(NMP)+NMPsdot

119870119873119872 and 119875 are the sizes of the scattered data119870 being theinterpolator length And the computational complexity of thekey part of the CG algorithm during an iteration is an orderof (NMP)log2(NMP) [18]

Table 1 Simulation parameters for full set of samples

Parameters ValuesCenter frequency (GHz) 91Bandwidth (GHz) 10Sampling interval along azimuth-range direction (m) 0004Number of samples along azimuth-range direction 64Sampling interval along elevation-range direction (m) 0004Number of samples along elevation-range direction 64

3 Results

The aforementioned algorithm is tested with numerical sim-ulations and experimental data The simulation parametersare shown in Table 1 Figure 3 shows the target model with8 point-like scatterers with equal radar cross section The 3Dimaging result (isosurface of minus13 dB relative to the maximumvalue) of WDA using the full sampling data and the resultof the proposed CS-based method using only 25 of thefull data are shown in Figures 4(a) and 4(b) respectivelyClearly even with a small subset of the full data the CS-based method can provide a more accurate imaging resultwith higher resolution than WDA

The experiments on real measured data are performed Astepped-frequencyW-band radar with two circular polarizedhorn antennas is used for the measurement which is shownin Figure 5 Three screws and a card are measured respec-tively as shown in Figure 6The diameter of the cross sectionof the screw is about 1 cm

The correspondingMMW imaging results ofWDA usingthe full measured data are shown in Figures 7(a) and 8(a)respectively And the results of the CS-based method usingonly 25 of the full data are demonstrated in Figures 7(b)and 8(b) respectively Due to the fact that the card is adistributed target the imaging result in Figure 8(b) is notso good as the point-like target in Figure 7(b) However themain characteristics remained for example the chip insidethe card can be easily seen in Figure 8(b)


minus01

0

01

minus01

0

01minus01

0

01

Range (m)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

(a)

minus01

0

01

minus01

0

01minus01

0

01

Range (m)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

(b)

Figure 4 3D MMW images of the target model (a) the result of WDA using the full data and (b) the result of the CS-based method usingonly 25 of the full data

Figure 5 W-band measurement radar

Figure 6 Photo of three screws and a card


Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus015

minus01

minus005

0

005

01

015

(a)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus015

minus01

minus005

0

005

01

015

(b)

Figure 7 MMW images of the screws (a) the result of WDA using the full data and (b) the result of the CS-based method using only 25of the full data

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus01

0

01

(a)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus01

0

01

(b)

Figure 8 MMW images of the card (a) the result of WDA using the full data and (b) the result of the CS-based method using only 25 ofthe full data

4 Conclusion

A CS-based method has been proposed for cylindricalnear-field 3D MMW imaging The imaging process and itsinversion are represented by an operator and its inversionrespectively to avoid large-scale matrix computation Thusthe CS approach can be applied to the cylindrical 3D imagingby using the operator as the sensing matrix Simulation andexperiment results show that the CS-based method can offer

highly accurate and reliable results even using only a smallsubset of the full samples compared with the traditionalwavenumber domain algorithm

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


References

[1] DM SheenD LMcMakin andT EHall ldquoThree-dimensionalmillimeter-wave imaging for concealed weapon detectionrdquoIEEE Transactions onMicrowaveTheory and Techniques vol 49no 9 pp 1581ndash1592 2001

[2] R Appleby andRNAnderton ldquoMillimeter-wave and submilli-meter-wave imaging for security and surveillancerdquo Proceedingsof the IEEE vol 95 no 8 pp 1683ndash1690 2007

[3] D M Sheen D McMakin and T E Hall ldquoNear-fieldthree-dimensional radar imaging techniques and applicationsrdquoApplied Optics vol 49 no 19 pp E83ndashE93 2010

[4] S S Ahmed A Genghammer A Schiessl and L-P SchmidtldquoFully electronic E-band personnel imager of 2 m2 aperturebased on a multistatic architecturerdquo IEEE Transactions on Mi-crowave Theory and Techniques vol 61 no 1 pp 651ndash657 2013

[5] D M Sheen and T E Hall ldquoReconstruction techniques forsparse multistatic linear array microwave imagingrdquo in Passiveand Active Millimeter-Wave Imaging XVII vol 9078 of Proceed-ings of SPIE p 12 June 2014

[6] E J Candes J Romberg and T Tao ldquoRobust uncertaintyprinciples exact signal reconstruction from highly incompletefrequency informationrdquo IEEE Transactions on InformationThe-ory vol 52 no 2 pp 489ndash509 2006

[7] D L Donoho ldquoCompressed sensingrdquo IEEE Transactions onInformation Theory vol 52 no 4 pp 1289ndash1306 2006

[8] R G Baraniuk and P Steeghs ldquoCompressive radar imagingrdquoin Proceedings of the IEEE Radar Conference pp 128ndash133 April2007

[9] L C Potter E Ertin J T Parker and M Cetin ldquoSparsity andcompressed sensing in radar imagingrdquo Proceedings of the IEEEvol 98 no 6 pp 1006ndash1020 2010

[10] X Zhang P Huang and X Li ldquo2D SAR imaging scheme basedon compressive sensingrdquo Electronics Letters vol 50 no 2 pp114ndash116 2014

[11] W J Zhang and A Hoorfar ldquoA generalized approach for SARand MIMO radar imaging of building interior targets withcompressive sensingrdquo IEEE Antennas and Wireless PropagationLetters vol 14 pp 1052ndash1055 2015

[12] D M Sheen D L McMakin T E Hall and R H SevertsenldquoReal-time wideband cylindrical holographic surveillance sys-temrdquo US Patent 5 859 609 1999

[13] S Sun G Zhu and T Jin ldquoNovel methods to accelerate CSradar imaging byNUFFTrdquo IEEE Transactions onGeoscience andRemote Sensing vol 53 no 1 pp 557ndash566 2015

[14] Y Nesterov Introductory Lectures on Convex Optimization ABasic Course Kluwer Academic Publishers BostonMass USA2004

[15] J A Tropp and A C Gilbert ldquoSignal recovery from randommeasurements via orthogonal matching pursuitrdquo IEEE Trans-actions on Information Theory vol 53 no 12 pp 4655ndash46662007

[16] M A T Figueiredo R D Nowak and S J Wright ldquoGradientprojection for sparse reconstruction application to compressedsensing and other inverse problemsrdquo IEEE Journal on SelectedTopics in Signal Processing vol 1 no 4 pp 586ndash597 2007

[17] A Beck and M Teboulle ldquoA fast iterative shrinkage-threshold-ing algorithm for linear inverse problemsrdquo SIAM Journal onImaging Sciences vol 2 no 1 pp 183ndash202 2009

[18] M Lustig D Donoho and J M Pauly ldquoSparse MRI theapplication of compressed sensing for rapid MR imagingrdquoMagnetic Resonance in Medicine vol 58 no 6 pp 1182ndash11952007

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RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



O

ElevationAntenna element

Azimuth

x

z

(x y z)

y

O120579998400

(R0 cos120579998400 y998400 R0 sin120579998400)

Figure 1 Cylindrical near-field 3D imaging configuration

Raw data

Elevation FFT

Azimuth IFFT

2D interpolation

3D IFFT

Complex image

Azimuth FFT

Azimuth FFT

divide

exp(jky y9984000)

exp(minusj2krR0)exp[minusj(radic4kr

2 minus ky9984002R0 cos(120579998400))]

Figure 2 Scheme of the wavenumber domain algorithm

2 CS-Based Method for 3D MMW Imaging

For the 3D imaging geometry is illustrated in Figure 1 Anobject formed by a distribution of independent scatterers ofreflectivity 119892(119909 119910 119911) is located at the center of the imagingscene The backscattered field 119884(119896 120579 119910

1015840) after demodulation

is given by

119884 (119896 120579 1199101015840) = ∭

119909119910119911

119892 (119909 119910 119911)

sdot exp [minus11989521198961198771205791199101015840 (119909 119910 119911)] d119909 d119910 d119911

(1)

where 119896 = 2120587119891119888 is the spatial frequency119888 represents the light speed 119877

1205791199101015840(119909 119910 119911) =

radic(1198770 cos 120579 minus 119909)2 + (1198770 sin 120579 minus 119911)2+ (1199101015840 minus 119910)

2 is the distancefrom each antenna element at (1198770 cos 120579 119910

1015840 1198770 sin 120579) to each

scattering center at (119909 119910 119911) and 1198770 is the radius of thecylindrical aperture as shown in Figure 1

The scheme of the traditional WDA [12] for near-fieldcylindrical 3D imaging is illustrated in Figure 2We representthe imaging process as an operator Then the inverse processcan be represented as the inversion of the operator Thus theimaging process is given by

119892 (119909 119910 119911) = 119866 [119884 (119896 120579 1199101015840)] (2)

where the operator 119866 denotes the imaging process as shownin Figure 2 that is

119866 = IFFT3D IN2D IFFT119896120579

FFT120579[FFT1199101015840 (sdot)]

sdot FFT120579exp [119895119896

1199091199111198770 cos (120579)]

(3)

where IN2D(sdot) represents 2D interpolation


minus005

0

005 minus0050

005

minus005

0

005

Azimuth-range (m)

Range (m)

Elev

atio

n-ra

nge (

m)



as follows

119884 (119896 120579 1199101015840) = 119866

minus1[119892 (119909 119910 119911)] (4)





min119892

1003817100381710038171003817120595119892 (119909 119910 119911)10038171003817100381710038170

st 119884 (119896 120579 1199101015840) = 119866

minus1[119892 (119909 119910 119911)]

(5)



min 10038171003817100381710038171003817119884 (119896 120579 119910

1015840) minus119866minus1

[119892 (119909 119910 119911)]10038171003817100381710038171003817

22

+1205821003817100381710038171003817120595119892 (119909 119910 119911)

10038171003817100381710038171

(6)









3 Results





minus01

0

01

minus01

0

01minus01

0

01

Range (m)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

(a)

minus01

0

01

minus01

0

01minus01

0

01

Range (m)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

(b)





Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus015

minus01

minus005

0

005

01

015

(a)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus015

minus01

minus005

0

005

01

015

(b)


Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus01

0

01

(a)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus01

0

01

(b)


4 Conclusion






References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus005

0

005 minus0050

005

minus005

0

005

Azimuth-range (m)

Range (m)

Elev

atio

n-ra

nge (

m)



as follows

119884 (119896 120579 1199101015840) = 119866

minus1[119892 (119909 119910 119911)] (4)





min119892

1003817100381710038171003817120595119892 (119909 119910 119911)10038171003817100381710038170

st 119884 (119896 120579 1199101015840) = 119866

minus1[119892 (119909 119910 119911)]

(5)



min 10038171003817100381710038171003817119884 (119896 120579 119910

1015840) minus119866minus1

[119892 (119909 119910 119911)]10038171003817100381710038171003817

22

+1205821003817100381710038171003817120595119892 (119909 119910 119911)

10038171003817100381710038171

(6)









3 Results





minus01

0

01

minus01

0

01minus01

0

01

Range (m)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

(a)

minus01

0

01

minus01

0

01minus01

0

01

Range (m)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

(b)





Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus015

minus01

minus005

0

005

01

015

(a)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus015

minus01

minus005

0

005

01

015

(b)


Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus01

0

01

(a)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus01

0

01

(b)


4 Conclusion






References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus01

0

01

minus01

0

01minus01

0

01

Range (m)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

(a)

minus01

0

01

minus01

0

01minus01

0

01

Range (m)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

(b)





Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus015

minus01

minus005

0

005

01

015

(a)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus015

minus01

minus005

0

005

01

015

(b)


Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus01

0

01

(a)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus01

0

01

(b)


4 Conclusion






References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus015

minus01

minus005

0

005

01

015

(a)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus015

minus01

minus005

0

005

01

015

(b)


Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus01

0

01

(a)

Azimuth-range (m)

Elev

atio

n-ra

nge (

m)

minus01 0 01

minus01

0

01

(b)


4 Conclusion






References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article cylindrical three-dimensional millimeter-wave imaging...

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