building feature extraction method based on double reflection imaging … · 2019. 10. 11. ·...

Deng et al. EURASIP Journal on Wireless Communications and Networking (2019) 2019:231 https://doi.org/10.1186/s13638-019-1530-1

RESEARCH Open Access

Building feature extraction method based

on double reflection imaging dictionary

Honggao Deng1,2, Tingfa Xu1*, Qinghua Liu2 and Yuhan Zhang1

Abstract

In the technology of building feature extraction, multi-path virtual image appears in the imaging result because theimaging scene is composed of complex wall model and the observation distance of the through-wall radar is short.In order to solve this problem, this paper proposes a double reflection imaging dictionary algorithm to extractbuilding scattering center. In this algorithm, the propagation models of direct path and double reflection path areestablished with the direct path imaging dictionary and the double reflection imaging dictionary, the correspondingoptimization problems are constructed. Finally, the multi-perspective fusion imaging steps are taken to suppress thefalse image according to the non-correlation of false image from the different reflection path. Experimental resultsverify the effectiveness of the proposed algorithm.

Keywords: Through-the-wall radar imaging (TWRI), The direct path imaging dictionary, The double reflection imagingdictionary, Building dominant scatterers

1 IntroductionUWB through-wall-radar imaging (TWRI) is a new tech-nology in recent years, which can obtain high resolutionimages of buildings all day [1]. TWRI technology can de-termine the layout of buildings and identify indoorlocation information, which has wide practical value indisaster relief, counter-terrorism operations and fireprotection [2]. At present, most TWRI systems observethe building’s wall imaging by multi view [3, 4], and thelayout of the building is achieved by the radar imagefusion method. This treatment will cause that the layoutof the buildings is not intuitive enough, and the wallscannot match each other with lots of image thorn. A fewTWRI systems use the electromagnetic characteristics ofscatterers to extract the main scattering objects from thewall echo data, and get clear and complete layout imagesby graph theory, and overcome the influence of clutterand multipath [5–7]. This paper also focuses on thistype TWRI system.Most of the energy in the building scene is only

provided by a few strong scattering centers, which arecorners, indicating that the parameter space of radar

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* Correspondence: [email protected] Laboratory of Photoelectronic Imaging Technology and System, BeijingInstitute of Technology, Beijing, ChinaFull list of author information is available at the end of the article

echo in the corner scattering center is of high sparsity[8, 9]. Therefore, building corners can be extracted bycompressive sensing theory. In recent years, someresearch institutions have applied the compressive sens-ing theory to the TWRI system, and proposed manypractical and efficient imaging algorithms. They dividedthe building scene into multiple grid points, assumingthat the corner can be located at any grid point of thescene, and achieved the better imaging effect [4–7].In [4], a ghosting suppression method based on corner

azimuth features is proposed. This method fuses mul-tiple sub-aperture images with full-aperture images toeliminate multiple aperture ghosting. However, a largenumber of antenna arrays should be set around build-ings, and the performance of this method is greatlyinfluenced by the number and orientation of the antennaarray. In practical application, it is difficult to select theproper azimuth of the sub-aperture and the number ofelectromagnetic wave data acquisition is huge, so themethod is not practical.In order to reduce the number of data collection and

time, and increase the scattering signal in the corner ofthe building, oblique illumination is considered, whichspecially enhances the radar returns from the cornersformed by the orthogonal intersection of two walls [5–7].In [7], an oblique MIMO radar antenna array is used to

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Fig. 1 The simulation scenario

Deng et al. EURASIP Journal on Wireless Communications and Networking (2019) 2019:231 Page 2 of 9

reduce the sidelobe of the corner, and the layout of thebuilding through the corner location information is indir-ectly obtained. However, the wall compensation step isemployed to compensate for the delay of the wall parallelto the antenna array, which is not applicable to theoblique antenna array, resulting in the deviation of cornerposition. In [6, 7], the influence of azimuth of antennas onbuilding scatterers is considered, and an over completedictionary based on antenna azimuth variables is pro-posed, which can completely restore location informationof main scatters. However, the method in [7] considersthe corner of a building as a simple point target, while thecorner should be regarded as an extended target when de-tecting the building in the near field. This method fails totake into account the dihedral angle attribute of thecorner and ignores the double reflection phenomenon ofthe corner echo, resulting in defocus, background noise,and more wall clutter in the corner imaging.When using through-wall radar test building, the

phenomenon of multipath effect exists in the actualenvironment. Antenna array receives not only the cornerdirect reflection echo signal, but also multipath trans-mission signals from the wall reflection and the secondreflection signals from the corner. If the informationcontained in the double reflection wave of the corner isused as the supplement of the corner information, thefalse image can be effectively suppressed while the signalstrength of the corner is strengthened.From this point of view, in this paper, a combined

algorithm based on direct wave dictionary and secondarywave dictionary is proposed to extract the scatteringcenter of buildings and remove the multi-path ghost.Firstly, the corner is regarded as the extended target,and the direct path model and the double reflectionmodel are constructed based on corner characteristics.Each path is regarded as an observation channel andconcentrated on the same compressed sensing model.Then the direct path imaging dictionary and the doublereflection imaging dictionary are constructed, and thesingle view imaging is obtained by using the compressedsensing method. Finally, the multi-perspective fusion im-aging is used to suppress the false image. The methodcan not only make full use of the double reflection infor-mation of the corner to accurately extract the scatteringcenter of the building, but also use the non-correlationof false image from the different reflection path tosuppress a large number of false images and noises. Thesimulation and real data are used to prove the validity ofthe proposed approach.This method can not only make full use of the informa-

tion of corner echo to accurately extract the scatteringcenter of buildings, but also use the false image non-correlation of different observation models to suppress alarge number of false images and noises. Simulation and

experimental results verify the effectiveness and feasibilityof the proposed method.The rest of the paper is organized as follows. In Section

II, the direct path model and the double reflection modelare introduced. In Section III and Section IV, the detailedprocessing steps of the proposed imaging dictionary andimage fusion algorithm are described. In Section V, theGprMax simulation data and the real experimental dataare provided to evaluate the performance of the proposedalgorithm. The conclusions are drawn in Section VI.

2 ResultsIn this section, several computer simulation and real datacollection experiment results are provided to validate theproposed algorithm.

2.1 Simulation resultsAs shown in Fig. 1a, 2.00 m × 2.00 m square buildingmodel is established including six walls and four corners,the walls are 0.10-m thick and made of solid concretewith permittivity of 4.5. The transceiver array is 2.00 mfrom the corner of the building, and the antenna array isoblique to the walls, as shown in Fig. 1. The simulateddata is obtained using GprMax simulation. A stepped-frequency signal consisting of 201 frequencies coveringthe frequency band of 1–2 GHz was used for interrogat-ing the scene. The inter-element spacing of sensorsis 0.10 m. In this simulation, we study the performanceof the proposed algorithm for the case when only thepath L1 exist. In the unknown position of the corner, weassume that the corners can be located at any pixel ofthe image and all corners have the same orientationangle, which is determined by the oblique illuminationunder consideration [7], so we set the orientation angle

of the scatterers ϕp ≈ 0° [9] and angular tilt of the arrayϕp, n ∈ [0°, 90°]. The oblique antenna array is used to re-

Fig. 3 The image from double reflection path


duce the echo of the wall. In this simulation, the angulartilt of the array baseline is 45°, we can get better resultswhen the tilt angle is set to the range of [30°, 60°].The scene grid is meshed by interval 0.10 m × 0.10 m,

and the discrete observation equation of radar receivedsignal is derived based on the direct propagation pathmodel and the double reflection propagation pathmodel. Imaging result considering only the direct path isshown in Fig. 2. The image with respect to only threedouble reflection imaging dictionary is shown in Fig. 3.The image fusion result is shown in Fig. 4. It is clear

that the multipath noises have been deleted completelyand the location and strength of the corner can be de-tected correctly from Fig. 4. Using the algorithms of [7],although the corner location can be roughly identified,there exists the phenomenon of defocus, noise, and wallclutter shown in Fig. 5.In order to more directly analyze the performance of

the proposed algorithm, three evaluation criteria oftarget-to-clutter ratio (TCR), signal-to-clutter ratio(SCR), and entropy of the image (ENT) are provided inTable 2. The TCR value of an image is defined as theratio between the highest pixel intensity value of the truecorner location area to the maximum pixel intensityvalue of the clutter area. The higher the TCR value, theclearer the target is relative to the background clutter[14]. The ENT value of an image determines the com-plexity of imaging, and the ENT value is smaller whenthe whole graph is less clutter. The SCR value of animage is the ratio of the power in the target regions tothe power summation of the rest regions. When thebackground noise is more fully suppressed and the qual-ity of the imaging results is better, the SCR is larger.In Table 1, the ENT value of [7] is larger, and the clut-

ter of the image is much more. We observe that theTCR value and the SNR value of this method are larger,

Fig. 2 The image from direct path

the target relative background clutter is stronger, thebackground noise is suppressed sufficiently, and thequality of the imaging results is better, thus improvingthe detection performance.

2.2 Experimental resultsIn order to verify the reconstruction effect of the pro-posed algorithm in the actual radar data, a radar test sys-tem was constructed by using vector network analyzerand horn antenna. The system configuration diagram andthe measured scene are shown in Fig. 6. The experimentalscene geometry is depicted in Fig. 7. The thickness of thewall is 0.20 m and relative permittivity of 6.4. The widthof the front wall and the side walls are 2.45 m and 2.40 m,respectively. This radar test system is placed 1.00 m fromthe corner of the building. Four sets of experimental dataare tested in the experiment with a sample shown in Fig. 7.The tilt angular of the array baseline is 45°. The radar

Fig. 4 The fusion result

Fig. 5 The image result of [7]Fig. 6 Photograph of the experimental scene


antenna installed on the car forms a 1.80 m long syntheticaperture, and the interval between adjacent antennasis 0.10 m. The stepped frequency continuous waveform isemployed [15], with the frequency starting from 1 GHz to2 GHz with the frequency interval 10 MHz.The multi-viewpoint imaging results of direct path

imaging dictionary and double reflection imaging dic-tionary are shown in Figs. 8 and 9, respectively. The finalfusion result is shown in Fig. 10. It is clear that thenoises have been deleted completely and the locationand strength of the corner can be detected correctly. Asshown in Fig. 11 with the algorithms of [7], although thecorners of interest are visible in the image, it is difficultto discriminate them from other scatterers and clutter.As can be seen from Table 2, the ENT values of [7] are

larger, the clutter of images is more, and the images arerelatively chaotic. At the same time, the TCR and SCRvalues of the proposed algorithm are larger, and the qual-ity of imaging results is better.

3 ConclusionsThis paper considers the problem of multipath ghostselimination for the through-wall radar imaging. In theexperiment of building feature extraction, while the obser-vation distance between radar and building is relativelycloser, the corner of a building is regarded as a complexscatter. So if the corner is regarded as a simple pointtarget to be extracted, the image will appear defocus andmore false images. In order to solve this problem, thedouble reflection imaging dictionary is proposed to extract

Table 1 Comparison of effect of simulation experiment

Algorithm TCR/dB ENT SCR/dB

The algorithm in [7] 1.6843 0.6518 − 10.0881

The proposed algorithm 2.4852 0.1157 − 0.2118

the scattering center of the building by building a directwave dictionary and the second reflection dictionary.Multi-perspective image fusion method is used to accur-ately identify the corner position of the building area,enhance the scattering amplitude of the corner, suppress alot of wall clutter and background noise. The processingresults of GprMax simulation data and experimental datashow that the whole image is relatively clear.

4 Methods4.1 TWRI signal modelAs shown in Fig. 12, the building model is a simple lay-out of three rooms with the walls of 0.1 m thickness.We consider a monostatic synthetic aperture radar im-aging system. The data acquisition is carried out in anoblique position, which significantly attenuates the wallreturns and enhances corner scatterers. Let the antennaat the nth location illuminates the scene with a stepped-frequency signal of M frequencies, and the mth fre-quency ωm is defined as

Fig. 7 The simulation scenario

Fig. 8 The image from direct path Fig. 10 The fusion result


ωm ¼ ω0 þmΔω;m ¼ 0;⋯;M−1 ð1Þ

where ω0 and Δω denote the lowest frequency in thebandwidth spanned by the stepped-frequency signal andthe frequency step size, respectively.

4.2 The direct propagation path signal modelAccording to the theory of physical optics, the responseof the scene can be modeled as the sum of responsesfrom individual corner scatterers, assuming that thescatterers do not interact with each other. Thus, the dir-ect path echo received by the nth transceiver at the mthfrequency can be represented as [6, 7]

yT m; nð Þ ¼XQp¼1

Sp m; n;ϕp� �

exp − jωmτAð Þp;n

� �þ w m; nð Þ ð2Þ

Fig. 9 The image from double reflection path

where Q is the number of corner scatterers present inthe illuminated scene, τðAÞp;n is the direct path two-waytraveling time of the signal from the nth antenna to thepth corner scatterer. The term w(m, n) in Eq. (2) modelsthe contributions of other wall scatterers, noise, and themultipath propagation effects. The canonical scatteringresponse Spðm; n;ϕpÞ of the pth corner reflector is givenby [7]

Sp m; n;ϕp� �

¼ Ap sinc ωmLpc sin ϕp;n−ϕp� ��

ð3Þ

where the variables Ap, Lp, and ϕp , respectively, definethe amplitude, length, and orientation angle of the pthcorner, and the variable ϕp, n denotes the aspect angleassociated with the pth corner reflector and the nthantenna. c = 3 × 108 m/s.

Fig. 11 The image of [7]

Table 2 Comparison of the effect of measured algorithm

Algorithm TCR/dB ENT SCR/dB

The algorithm in [7] 1.0288 0.4774 − 8.2636

The proposed algorithm 2.1964 0.2221 − 4.9635


When the antenna array obliquely illuminates the wall,the echo transmission path is shown in Fig. 13a, and thedirect path traveling time of the signal from the nthantenna to the pth corner scatterer can be representedas

τ Að Þp;n ¼2d0c

þ 2dffiffiε

p−1ð Þ

c � cosθ

¼2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixp−xn� �2 þ yp−yn� �2

rc

þ 2dffiffiε

p−1ð Þ

c � cosθ ð4Þ

where (xp, yp) denote the coordinates of the pth corner,d and ε are the thickness and relative permittivity of thewall, respectively θ is the tilting angle of the antennaarray.In the case of complex imaging scenes, the defocus

and virtual images will appear in the imaging results ifthe corner of the building is regarded as a simple pointtarget; therefore, the double reflection echo model of thecorner is introduced in this paper.

4.3 The double reflection propagation paths signal modelThe indoor walls cause that electromagnetic waves notonly travel between corners and antennas, but also re-flect many times between antennas and walls, whichmake the received signals appear multi path echo [10].For simplicity, the corner scattering center is regarded

Fig. 12 Building layout

as the dihedral and the double reflection characteristicsof the corner are the major issues that will be discussedin this paper, as shown in Fig. 13b. The double reflectionecho is similar to the first-order multipath effect in thebuilding. We assume that there are totally K double re-flection propagation paths in the effective range dfinite ofthe corner, which are expressed as path L1, L2, ⋯, LK,respectively [11]. Let y Jk ðm; nÞ represents the double re-flection echoes received by the path Lk at the mth fre-quency of the nth transceiver. Thus, the doublereflection echoes received by the nth transceiver at themth frequency can be written as

y J m; nð Þ ¼XKk¼1

y Jk m; nð Þ

¼XKk¼1

XQp¼1

Sp m; nð Þℑ xp; yph i

exp − jωmτ kð Þp;n� �

ð5Þwhere the function ℑ[xp, yp] works as an indicator func-tion with the pth corner. If the corner of the effectiverange is dfinite, and the distances between the doublereflection point and the pth corner meet jxp−xk1 j< dfinite , jxp−xk2 j < dfinite , jyp−yk1 j < dfinite , and jyp−yk2 j< dfinite four conditions in Eq. (7), ℑ[xp, yp] = 1. The ex-pression of the indicator function is given by

ℑ xp; yph i

¼ 1xp−xk1 < dfinite; and; xp−xk2 < dfinite; and;yp−yk1

< dfinite; and; yp−yk2 < dfinite

0 otherwise

8><>:

ð7ÞOther double reflections that do not satisfy this condi-

tion in Eq. (7) are not considered. The τðkÞp;n in Eq. (6)

Fig. 13 Electromagnetic wave reflection model for the corner. a The direct path propagation model. b The double reflection propagation path. cOne propagation path


describes the kth double reflection path traveling timefrom the nth antenna to the pth corner scatterer. Theelectromagnetic wave propagates along this path d1→

d2→ d3 shows in Fig. 13c, or vice versa. The τðkÞp;n is given

by

τ kð Þp;n ¼d1 þ d2 þ d3

cþ 2d

ffiffiε

p−1ð Þ

c � cosθ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixn−xk1ð Þ2 þ yn−yk1

� �2q þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixk1−xk2ð Þ2 þ yk1−yk2� �2q

þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixk2−xnð Þ2 þ yk2−yn

� �2qc

þ 2dffiffiε

p−1ð Þ

c � cosθð8Þ

where ðxk1 ; yk1Þ and ðxk2 ; yk2Þ represent the coordinatesof the two reflection points of the kth double reflection,respectively.Based on the above analysis, the total received signal

of building corner echoes is a combination of direct pathecho and the double reflection echoes returns, which isdescribed as

y m; nð Þ ¼ yT m; nð Þ þ y J m; nð Þ: ð9Þ

4.4 Sparse representation of the imageIn view of the corner model in the indoor environment,the direct path imaging dictionary and the double reflec-tion imaging dictionary are constructed based on thesparse description [10, 11], and the virtual images aresuppressed based on the non-correlation of noise in dif-ferent dictionaries.The building scene is divided into NX ×NY pixels. The

imaging dictionary AT corresponds to the direct trans-mission between the location of the antenna and thepixels in the corner of the building, which is called thedirect path echo dictionary. The imaging dictionary AJcorresponds to multiple double reflection transmissionbetween the location of the antenna and the pixels in

the corner of the building, which is called the double re-flection echo dictionary. The AT denotes the MN ×NXNY dimensional matrix and is expressed as

AT ¼S1;1 1; 1ð Þ S1;2 1; 1ð Þ ⋯ SNX ;NY 1; 1ð ÞS1;1 1; 2ð Þ S1;2 1; 2ð Þ ⋯ SNX ;NY 1; 2ð Þ

⋮ ⋮ ⋯ ⋮S1;1 M;Nð Þ S1;2 M;Nð Þ ⋯ SNX ;NY M;Nð Þ

2664

3775MN�NXNY

ð10Þ

where Si, j(m, n) represents the direct path echo samplein Eq. (11) between the nth transceiver at the mth fre-quency and the (i, j)th pixel point with the scatteringamplitude AAi; j and the corresponding direct propaga-

tion path time delay τðAÞi; j in Eq. (12).

Si; j m; nð Þ ¼ AAi; j exp − jωmτ Að Þi; j� �

; ð11Þ

τ Að Þi; j ¼2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixi−xnð Þ2 þ y j−yn

� �2rc

þ 2dffiffiε

p−1ð Þ

c � cosθ : ð12Þ

The kth double reflection echo dictionary A J k is anMN ×NXNY dimensional matrix with the expressiongiven by

A J k ¼S Jk ;1;1 1; 1ð Þ S Jk ;1;2 1; 1ð Þ ⋯ S Jk ;NX ;NY 1; 1ð ÞS Jk ;1;1 1; 2ð Þ S Jk ;1;2 1; 2ð Þ ⋯ S Jk ;NX ;NY 1; 2ð Þ

⋮ ⋮ ⋯ ⋮S Jk ;1;1 M;Nð Þ S Jk ;1;2 M;Nð Þ ⋯ S Jk ;NX ;NY M;Nð Þ

2664

3775MN�NXNY

ð13Þ

where S Jk ;i; jðm; nÞ is the kth double reflection echo sam-ple of the mth frequency between the nth transceiver

from the (i, j)th pixel point in Eq. (14). τðkÞi; j is the corre-sponding double reflection propagation path delay withthe same form as Eq. (8), and Ak represents the scatter-ing amplitude of the double reflection propagation pathof the (i, j)th pixel point.


S Jk ;i; j m; nð Þ ¼ Ak exp − jωmτ kð Þi; j� �

ð14Þ

τ kð Þi; j ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixn−xkið Þ2 þ yn−yki

� �2q þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixki;1−xki;2� �2 þ yk j;1−yk j;2� �2

r

þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixki;2−xn� �2 þ yk j;2−yn� �2

rc

þ 2dffiffiε

p−1ð Þ

c � cosθð15Þ

where ðxki;1 ; yk j;1Þ and ðxki;2 ; yk j;2Þ represent the coordi-nates of the two reflection points of the kth double re-flection correspond to the (xk, yk), respectively. Bystacking all the received signal y(m, n) in one columnvector, we obtain the radar observation vector with thefollowing expression

y ¼ y 1; 1ð Þ; y 1; 2ð Þ;⋯; y M;Nð Þ½ �T : ð16ÞThe real imaging scenario can be estimated based on

the received signal y which can be written as

y ¼ ATxT þXKk¼1

A J kxk : ð17Þ

where xT and xk are defined as the scattering coefficientvector. The multiple scene estimation images can beobtained according to multiple dictionaries. Assuming thatNXNY is much larger than MN, we can conclude that ATand A J k are only row full rank matrices. The dictionary ofdirect wave imaging is represented by ADPD, where ADPD =AT and A

þDPD represents the pseudo-inverse of ADPD.

Multiply both sides of Eq. (17) byAþDPD, we can derive

AþDPDy ¼ AþDPD ATxT þXKk¼1

A J kxk

!

¼ AþDPDATxT þ AþDPDA J1x1þ AþDPDA J2x2 þ AþDPDA J3x3 þ⋯ ð18Þ

where AþDPDATxT has a larger value, AþDPDA J1x1 also has a

certain pixel value, the other terms are very small. Sincethe corner of the building is regarded as an extended tar-get, not a scatter point target, AþDPDA J1x1 represents thecorresponding multipath ghost image to path L1. Similarly,AþDPDA J2x2 and A

þDPDA J3x3 are respectively the multipath

ghost images related to path L2 and path L3. Assuming Φyis the measurement matrix, the scene imaging results ofthe direct path imaging dictionary can be obtained bysolving sparse signal recovery problem in Eq. (19) [12].

xT ¼ arg minx

xTk k0 s:t ŷ−ΦyADPDxT

2

2 ≤ε0

ð19Þ

Let AðkÞMPD be the kth double reflection imaging diction-

ary, where AðkÞMPD ¼ A J k , and AðkÞþMPD represents the

pseudo-inverse. Multiply both sides of Eq. (17) by AþDPD,we can derive

A kð ÞþMPDy ¼ A kð ÞþMPDATxT þ A kð ÞþMPDA J1x1þ A kð ÞþMPDA J2x2 þ A kð ÞþMPDA J3x3 þ⋯ ð20Þ

where AðkÞþMPDA J kxk represents the corresponding multi-path image to double reflection path Lk. The sceneimaging results of the kth double reflection imagingdictionary can be obtained by solving sparse signal re-covery problem in Eq. (21).

xk ¼ arg minx

xkk k0 s:t ŷ−ΦyA kð ÞMPDxk

2

2≤ε1

ð21Þ

OMP algorithm is used to solve the problem of sparsesignal recovery of Eqs. (19) and (21).

4.5 Image fusion of multiple dictionariesBased on the above analysis, both the estimated imagederived from the direct path imaging dictionary and theestimated images produced by the double reflection im-aging dictionaries contain the target image of interest.Moreover, the elements will form a highlight focused re-gion located at the position of the true target, and thenoise in these images will not overlap [15].In order to extract the building corner and delete the

noise, we fuse these estimated images together. Based onthe above features, these images are fused by a non-coherent image fusion method to produce a no-falseimage. To be clear, for the image xT and x1 of this ex-ample, only the path L1 is considered, we derive

x f ;1 ¼ xTj j � x1j j ¼ AþDPDATxT þ AþDPDA J1x1 � A 1ð ÞþMPDATxT þ A 1ð ÞþMPDA J1x1

¼ AþDPDATxT � A 1ð ÞþMPDATxT þ AþDPDA J1x1 � A 1ð ÞþMPDA J1x1 þAþDPDATxT � A 1ð ÞþMPDA J1x1 þ AþDPDA J1x1 � A 1ð ÞþMPDATxT

ð22Þ

where xf, 1 denotes the fusion result of image xT and x1,|·| represents the absolute value operation. By inspectingEq. (22), we could observe that AþDPDATxT and A

ð1ÞþMPDA J1

x1 are the target images derived from the direct path im-aging dictionary and the first double reflection imaging

dictionary, respectively. AþDPDA J1x1 and Að1ÞþMPDATxT are

the fake images and noise with respect to the direct pathimaging dictionary and the first double reflection im-aging dictionary, respectively. It is clear that the third

item jAþDPDATxT j � jAð1ÞþMPDA J1x1j represents the genuinetarget image, and the other three items are approxi-mated to zeros. In the same way, we obtain xf, k whichdenotes the fusion result of image xT and xk from thepath Lk of the double reflection echoes in the corner.


Three double reflections are taken into account, and theexpression of the fused image xf is described as below

x f ¼ x f 1 � x f 2 � x f 3 ≈ AþDPDATxT 3

� A 1ð ÞþMPDA J1x1 � A 2ð ÞþMPDA J2x2 � A 3ð ÞþMPDA J3x3 ð23Þ

where xf represents the fusion result of image xT, x J1 ,x J2 , and x J3 . When radar detection is performed aroundthe building, it is necessary to incoherent fusion of im-ages from multiple-viewpoint, we have

x f ‐sum ¼ x f ‐A þ x f ‐B þ x f ‐C þ x f ‐D ð24Þwhere xf ‐ sum denotes the fusion result of image xf ‐ A, xf ‐B, xf ‐ C, and xf ‐D, which are respectively the image de-rived from the four single-location image, as shown inFig. 12.

AbbreviationsENT: Entropy of the image; OMP: Orthogonal matching pursuit; SCR: Signal-to-clutter ratio; TCR: Target-to-clutter ratio; TWRI: Through-the-wall radarimaging

AcknowledgementsThe authors would like to thank Tingfa Xu for the support.

Authors’ contributionsHD and TX conceived of the building feature extraction method based ondouble reflection imaging dictionary. All authors read and approved the finalmanuscript.

FundingThis work was supported by the Major Science Instrument Program of theNational Natural Science Foundation of China under grant 61527802.This work was supported by the Major Science and Technology Foundationof Guangxi Province under grant AA17204093.

Availability of data and materialsAll data are fully available without restriction.

Competing interestsThe authors declare that they have no competing interests.

Author details1Key Laboratory of Photoelectronic Imaging Technology and System, BeijingInstitute of Technology, Beijing, China. 2School of Information andCommunication, Guilin University of Electronic Technology (GUET), Guilin,China.

Received: 6 May 2019 Accepted: 25 July 2019

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Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.

AbstractIntroductionResultsSimulation resultsExperimental results

ConclusionsMethodsTWRI signal modelThe direct propagation path signal modelThe double reflection propagation paths signal modelSparse representation of the imageImage fusion of multiple dictionariesAbbreviations

AcknowledgementsAuthors’ contributionsFundingAvailability of data and materialsCompeting interestsAuthor detailsReferencesPublisher’s Note

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