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IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS 1
Initial Experimental Tests of an ANN-Based
Microwave Imaging Technique for
Neck Diagnostics
Chiara Dachena , Alessandro Fedeli ,Member, IEEE, Alessandro Fanti ,Member, IEEE,
Matteo B. Lodi ,Member, IEEE, Giorgio Fumera, Member, IEEE,
Matteo Pastorino ,Fellow, IEEE, and Andrea Randazzo ,Senior Member, IEEE
Abstract— In this letter, a microwave imaging strategy based
on an artificial neural network (ANN) is applied, for the first time,
to experimental data gathered from simplified neck phantoms.
The ANN is used for solving the underlying inverse scattering
problem, with the aim of retrieving the dielectric properties
of the neck for monitoring and diagnostic purposes. The ANN
is trained using simulated phantoms, to overcome the limited
availability of experimental data. First, a simple configuration
with a liquid-filled glass beaker is tested. Then, simplified 3-D-
printed models of the human neck are considered. The prelim-
inary findings indicate the possibility of training the network
with numerical simulations and testing it against experimental
measurements.
Index Terms—Artificial neural networks (ANNs), biomedical
imaging, inverse scattering, machine learning (ML), microwave
imaging (MWI).
I. INTRODUCTION
MICROWAVE imaging (MWI) emerged several decades
ago as a promising diagnostic technique for biomedical
applications [1]. Recently, besides the widespread applica-
tions related to breast tumor [2]–[5] and brain stroke detec-
tion [6]–[8], the use of MWI for other parts of the body,
such as torso and arms [9], [10], has gained attention, too.
Specifically, this work deals with MWI for diagnosing and
monitoring neck diseases, such as cervical myelopathy [11]
and tumors [12], [13]. Indeed, although magnetic resonance
imaging (MRI) and computerized tomography (CT) represent
the gold standard, they are either expensive or relying on ion-
izing radiations. MWI represents a complementary technique
that, due to its nonionizing nature and the possibility of using
cheap components, may allow frequent monitoring. Moreover,
Manuscript received 20 June 2022; accepted 22 July 2022. (Corresponding
author: Alessandro Fedeli.)
Chiara Dachena, Alessandro Fedeli, Matteo Pastorino, and
Andrea Randazzo are with the Department of Electrical, Electronic, Telecom-
munications Engineering and Naval Architecture (DITEN), University of
Genoa, 16145 Genoa, Italy (e-mail: chiara.dachena@edu.unige.it; alessandro.
fedeli@unige.it; matteo.pastorino@unige.it; andrea.randazzo@unige.it).
Alessandro Fanti is with the Department of Electrical and Electronic
Engineering, University of Cagliari, 09123 Cagliari, Italy, and also with
the Istituto Nazionale di Fisica Nucleare-CA, Complesso Universitario di
Monserrato, 09042 Cagliari, Italy (e-mail: alessandro.fanti@unica.it).
Matteo B. Lodi and Giorgio Fumera are with the Department of Electrical
and Electronic Engineering, University of Cagliari, 09123 Cagliari, Italy
(e-mail: matteob.lodi@unica.it; fumera@unica.it).
Color versions of one or more figures in this letter are available at
https://doi.org/10.1109/LMWC.2022.3194805.
Digital Object Identifier 10.1109/LMWC.2022.3194805
since it aims at reconstructing the dielectric properties from
scattered-field measurements, it also potentially provides addi-
tional diagnostic information.
MWI is based on the solution of a strongly ill-posed and
nonlinear inverse problem [1]. Several solving approaches,
based on quantitative [3], [14] or qualitative methods [15],
[16], have been developed. In this context, we developed in
[11] a quantitative technique based on a regularization proce-
dure in Lebesgue spaces for the diagnosis of cervical myelopa-
thy. Inversion methods based on machine learning (ML)
paradigms have also been recently devised [17], considering
both convolutional [18] and fully connected artificial neural
networks (ANNs) [19]. In particular, the applicability of a fully
connected ANN for neck tumor detection has been studied,
through numerical simulations, by us in [12]. Such an ANN
can be in principle applied also to other parts of the body,
provided that a proper training dataset is adopted. It is worth
noting that other ANNs have been tried on other body parts,
e.g., for breast cancer [19] and brain stroke detection [20].
Although ANNs have been found to be quite effective,
one of the main obstacles in their practical application is the
amount of data required in the training phase [21]. In fact,
in MWI, the requirement of massive quantities of data for the
training phase does not allow training ANNs with experimental
data only. For this reason, most works are limited to numerical
analyses or use data from well-known datasets (e.g., the
Fresnel one [22]–[28]), and few contributions make use of
custom experimental data in the test phase [20]. Therefore,
the application of ANNs to experimental data still represents
a great challenge, which needs to be faced to uncover the full
potential of ML for MWI.
The aim of this letter is to report some initial tests against
experimental data of an ANN that has been trained with
numerical models only. To the best of the authors’ knowledge,
this is the first time that a deep learning approach is used with
experimental data gathered from neck-mimicking phantoms.
This letter is organized as follows. An overview of the MWI
method and the ANN architecture is provided in Section II.
Preliminary experimental results are reported and discussed in
Section III. Section IV reports some concluding remarks.
II. OVERVIEW OF THE IMAGING METHOD
Let us consider the tomographic imaging system
summarized in Fig. 1. Sequally spaced antennas are located
around the neck on a circumference of radius rnand acquire
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2IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS
Fig. 1. Structure of the proposed MWI system and the inversion approach
based on a fully connected neural network.
measurements of the electric field with a multi-illumination,
multistatic, and multifrequency approach. In this configuration,
Sviews are considered, with M=S−1 receiving antennas
for each view, and data are measured at Ffrequencies.
Between the antennas and the neck, a layer of matching
medium (with dielectric permittivity εmm and electric
conductivity σmm)is present. The developed approach aims
at reconstructing the differences in the dielectric properties
inside the investigation domain Dtwith respect to a given
reference configuration. In the following, Ef,s,mdenotes
the difference between the z-component of the total electric
field due to the actual and reference configurations (for
the fth frequency, the sth view, and the mth measurement
point). Moreover, εr,nand σnare the differential dielectric
properties in the nth subdomain (n=1,...,Nt)in which
Dtis discretized. As it is well known, the retrieval of εr,n
and σnstarting from Ef,s,mconstitutes a nonlinear and
ill-posed inverse problem [1]. An ANN-based inversion
approach, originally proposed in [12], is adopted in this letter.
As shown in Fig. 1, the input of the network is an array
containing the real and imaginary parts of Ef,s,m,i.e.,I=
[RE1,1,1,...,REF,S,M,I{E1,1,1},...,I{EF,S,M}]t.
The ANN is composed of Khidden layers, each one
containing Lneurons characterized by a weight vector
Wk,land a bias bk,l, with k=1,...,Kand l=1,...,L.
The output Okof the kth layer is computed as in [12].
The output layer has 2Ntneurons (with weight vector
WK+1,land a bias bK+1,l)and a regression function
is added to predict the dielectric properties in the
investigation domain, which are contained in the output
array O=[εr,1,...,ε
r,Nt,σ
1,...,σ
Nt]t.The
output is computed as O=R[Wt
K+1,1OK+bK+1,1,...,
Wt
K+1,2NtOK+bK+1,2Nt]t,whereRis the rectified linear
unit (ReLu) activation function. The Adam method [29]
is used in the training phase to minimize the loss
function L=(1/Dtr)i(
εi
r,r−εi
r,a
/
εi
r,a
)+
i(
σi
r−σ i
a
/
σ i
a
),whereDtr is the number of
samples, εi
r,rand εi
r,aare the reconstructed and actual
real parts of the relative dielectric permittivity of the ith
sample, and σ i
rand σ i
aare the corresponding electric
conductivities.
III. PRELIMINARY EXPERIMENTAL RESULTS
Some preliminary experimental results are presented in this
section to test the reconstruction capability of the proposed
ANN. The adopted MWI system is described in [11]. It con-
sists of S=10 slotted cavity-backed bow-tie antennas and
a vector network analyzer connected to the antennas through
a switch matrix. A mixture of water and 70% glycerin (vol-
umetric), enclosed in polyethylene bags interposed between
the antennas and the phantom, is used as matching medium.
Fig. 2. Configuration of the experimental target and reconstructed maps.
(a) Beaker. (b) εr.(c)σ . (d) 3-D printed neck “phantom 1” [11]. (e) εr.
(f) σ . (g) 3-D printed neck “phantom 2” [11]. (h) εr.(i)σ .
F=4 frequencies between 600 and 750 MHz with 50-MHz
frequency step have been considered for the first two cases,
whereas for the third case, F=7 frequencies between 600 and
900 MHz have been used. Such parameters have been chosen
based on the analysis performed in [11], where it has been
found that frequencies between 500 and 1 GHz, with a match-
ing medium having relative dielectric permittivity between
5 and 60, provide a good tradeoff between low reflection
from skin and high penetration into the neck. The developed
network has K=5 hidden layers and L=448 neurons for
each layer. Such parameters have been chosen according to the
analysis performed in [12]. The initial weights of the ANN are
drawn from a Gaussian distribution with zero mean value and
standard deviation equal to 10−2, whereas the initial biases are
set to zero. A constant L2norm regularization parameter equal
to 10−4is adopted to avoid overfitting, with a mini-batch size
of 256. An initial learning rate equal to 10−3is used in the
Adam method, with a maximum of 500 epochs.
In the first case, a circular glass beaker with external radius
rb=53.5 mm filled with a 70% glycerin:water mixture
and containing a circular inclusion with radius ri1=8.5
mm placed at (23,3)mm is considered [see Fig. 2(a)]. The
inclusion is filled with an 80% glycerin:water mixture. The
dielectric properties of these mixtures have been estimated
from reflection measurements performed on a liquid-filled
section of a short-circuited coaxial line [11]. The network
has been trained using a dataset of D=10 000 numerically
simulated configurations. Since the aim is to detect just the
inclusion inside the phantom, each target is modeled as a
circular cylinder with radius rn=6.2 cm (to account for
beaker and matching medium) and dielectric properties εmm =
43ε0S/m and σmm =0.8 S/m [11], in which a cylindrical
inclusion with random radius rt1∈(5,10)mm and position
(inside the beaker) is present. The dielectric permittivity of the
inclusion randomly ranges from 30ε0to 40ε0and its electric
conductivity is in the range [0.4,0.7]S/m. The investigation
domain is discretized into Nt=3024 square cells of side
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DACHE NA et al.: INITIAL EXPERIMENTAL TESTS OF AN ANN-BASED MWI TECHNIQUE FOR NECK DIAGNOSTICS 3
2 mm. The scattered fields are computed with a custom solver
based on the method of moments [30]. A subset of 90% of
samples is used to train the network, whereas the remaining
ones are used for validation. The obtained values of the loss
function are 1.03 and 1.1 for the training and validation sets,
respectively. The reference configuration is the phantom with-
out the inclusion, i.e., a homogenous circular structure with
dielectric properties equal to those of the matching medium.
In order to use the experimental data for testing the
ANN, a scattered-field calibration has been performed [31],
where the fields measured in the presence of a known
target are used to derive a set of scaling coefficients,
one for each transmitter–receiver pair and frequency. The
calibrated measurements are then obtained as Ef,s,m=
EM
f,s,mESI,R
f,s,mEM,R
f,s,m,whereEM
f,s,mare the uncalibrated
data and EM,R
f,s,mand ESI,R
f,s,mare the experimental and simu-
lated fields for the calibration target, respectively. In particular,
in this case, the calibration target is a circular inclusion with
radius ri2=6.2 mm that has been placed inside the beaker at
(23,5)mm. The reconstructions of εrand σ are reported
in Fig. 2(b) and (c). The internal inclusion is correctly local-
ized, and a quite good estimation of the dielectric properties
is obtained although εris underestimated.
In the second test case [see Fig. 2(d)], a 3-D-printed model
of the human neck is considered (“phantom 1” of [11]).
The considered printed structure contains some of the main
anatomical details, such as the air-filled trachea in the anterior
part of the neck and the external fat layer [11]. The 3-D-
printing material is polylactic acid (PLA), whose dielectric
properties are εPLA =3ε0and σPLA =0.001 S/m. The trachea
is characterized by εtra =ε0,σtra =0 S/m, and the neck filling
has εneck =43ε0and σneck =0.8 S/m. An inclusion with
radius rs1=12 mm has been placed inside the neck phantom
at (10,5)mm. The network has been trained by using a dataset
built from a numerical model of the phantom (containing
the external layer and the trachea), in which inclusions with
different random positions (inside the inner part) and radius
rt2∈(3,15)mm have been located. The dielectric properties
vary in the same ranges of the previous case. The reference
scenario is the phantom without inclusions. To calibrate the
data, an inclusion with radius rs2=5 mm has been placed
at (10,9)mm. The reconstructed values of εrand σ are
shown in Fig. 2(e)–(f). In this case, too, the inclusion is well
detected, although εris slightly overestimated and σ is
underestimated.
Finally, a more complex 3-D-printed model with vertebral
column filled with glycerin (εver =9.77ε0and σve r =
0.36 S/m) is considered [“phantom 2” of [11], Fig. 2(g)].
A circular printed inclusion with radius rv1=5mmhas
been located inside the vertebra at (0.5,0)mm. The numerical
models used in the training procedure reproduce the printed
structure and contain random inclusions inside the vertebra
with radius in the range rt3∈(3,12)mm. The ranges of the
dielectric properties are the same as before, and the structure
without inclusion is used as a reference scenario. To calibrate
the data, an inclusion with radius rv2=9 mm has been
considered inside the vertebra at (5,0)mm. The reconstructed
maps of the dielectric properties are shown in Fig. 2(h)–(i).
Even in this more involving case, the inclusion is well detected
in both εrand σ , and the reconstructed values are quite
accurate.
TAB L E I
RELATIVE RECONSTRUCTI ON ERRORS (DIMENSIONLESS)
For completeness, the performances of the approach have
been evaluated using the mean relative errors e{tot,b,in},γ =
(1/N{t,b,in})rn∈D{t,b,in}(|γrec(rn)−γact (rn)|/|γact(rn)|),where
γrec and γact are the reconstructed and actual values of εror
σ , respectively, rnis the center of the nth cell of the inves-
tigation domain, D{b,in}is the background (b)or the inclusion
(in)region, and N{b,in }is the corresponding number of cells.
Moreover, the relative errors on the estimated radius and center
of the inclusion have been evaluated, too. In particular, the
radius error, er, is computed as er=|rr−ra|/|ra|,wherera
and rrare the actual and estimated radiuses, respectively, the
latter obtained by setting a threshold equal to 40% on the
maximum reconstructed value of εr. Similarly, the center
errors, ecd,xand ecd,y, are the relative errors on the xand
ycoordinates of the reconstructed inclusion. The errors are
reported in Table I for the three considered cases. In the
second configuration, etot,εrand etot,σ and eb,εrand eb,σ are
slightly higher than in the first case. Indeed, in Fig. 2(e)–(f),
some artifacts in the background are present. Moreover, ein,σ
is about twice the value of the first case, and this is motivated
by the underestimation of the reconstructed values of σ .
In all cases, low radius and position errors are obtained, thus
allowing to identify and locate the inclusion suitably. In the
last case, errors are generally comparable with the simplest
configuration.
Finally, the robustness of the method with respect to uncer-
tainties in the values of the dielectric properties used in the
training set was tested (considering test cases #1 and #2).
In particular, the network has been trained with a model having
a variation of ±5% of the dielectric properties (outside the
inclusion). The average increase in the relative errors is 2.45%
for etot,εrand 9.15% for etot,σ .
IV. CONCLUSION
In this letter, initial experimental tests of an ANN approach
for quantitative MWI of the human neck have been discussed.
The considered ANN, which is composed of fully connected
layers, has been trained by means of numerical simulations and
then tested, for the first time, against experimental data. Three
different phantoms with inclusions have been considered: a
liquid-filled glass beaker, and a simplified and a complex
3-D-printed model of the human neck. The preliminary results,
although obtained with simplified phantoms in a laboratory
environment, are promising. In all cases, it has been possible
to identify with quite good accuracy position, dimension,
and dielectric properties of the inclusion, as summarized in
Table I. Future works will be aimed at a more extensive
analysis of the performance, also including more advanced
phantoms and possibly real necks. More complex neural
network architectures will be considered, too. The potential
extensions of the approach to other frequency bands (with the
necessary tradeoffs in terms of attainable accuracy) and to
different parts of the body will be addressed, too.
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4IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS
REFERENCES
[1] M. Pastorino and A. Randazzo, Microwave Imaging Methods and
Applications. Boston, MA, USA: Artech House, 2018.
[2] N. K. Nikolova, “Microwave imaging for breast cancer,” IEEE Microw.
Mag., vol. 12, no. 7, pp. 78–94, Dec. 2011, doi: 10.1109/MMM.
2011.942702.
[3] N. Abdollahi, I. Jeffrey, and J. LoVetri, “Improved tumor detection
via quantitative microwave breast imaging using eigenfunction-based
prior,” IEEE Trans. Comput. Imag., vol. 6, pp. 1194–1202, 2020, doi:
10.1109/TCI.2020.3012940.
[4] M. A. Aldhaeebi, K. Alzoubi, T. S. Almoneef, S. M. Bamatraf, H. Attia,
and O. M. Ramahi, “Review of microwaves techniques for breast
cancer detection,” Sensors, vol. 20, no. 8, p. 2390, Apr. 2020, doi:
10.3390/s20082390.
[5] S. Hosseinzadegan, A. Fhager, M. Persson, and P. M. Meaney, “Appli-
cation of two-dimensional discrete dipole approximation in simulating
electric field of a microwave breast imaging system,” IEEE J. Electro-
magn., RF Microw. Med. Biol., vol. 3, no. 2, pp. 80–87, Jun. 2019, doi:
10.1109/JERM.2018.2882689.
[6] A. T. Mobashsher and A. Abbosh, “Development of compact directional
antenna utilising plane of symmetry for wideband brain stroke detection
systems,” Electron. Lett., vol. 50, no. 12, pp. 850–851, Jun. 2014, doi:
10.1049/el.2014.0616.
[7] I. Sarwar et al., “Low-cost low-power acceleration of a microwave
imaging algorithm for brain stroke monitoring,” J. Low Power Electron.
Appl., vol. 8, no. 4, p. 43, Nov. 2018, doi: 10.3390/jlpea8040043.
[8] A. Fedeli, V. Schenone, A. Randazzo, M. Pastorino, T. Henriksson, and
S. Semenov, “Nonlinear S-parameters inversion for stroke imaging,”
IEEE Trans. Microw. Theory Techn., vol. 69, no. 3, pp. 1760–1771,
Mar. 2021, doi: 10.1109/TMTT.2020.3040483.
[9] A. Zakaria, A. Baran, and J. LoVetri, “Estimation and use of prior
information in FEM-CSI for biomedical microwave tomography,” IEEE
Antennas Wireless Propag. Lett., vol. 11, pp. 1606–1609, 2012, doi:
10.1109/LAWP.2012.2237537.
[10] D. Gibbins, D. Byrne, T. Henriksson, B. Monsalve, and I. J. Craddock,
“Less becomes more for microwave imaging: Design and validation of
an ultrawide-band measurement array,” IEEE Antennas Propag. Mag.,
vol. 59, no. 5, pp. 72–85, Oct. 2017, doi: 10.1109/MAP.2017.2731198.
[11] C. Dachena, A. Fedeli, A. Fanti, M. B. Lodi, M. Pastorino, and
A. Randazzo, “Microwave imaging for the diagnosis of cervical dis-
eases: A feasibility analysis,” IEEE J. Electromagn., RF Microw. Med.
Biol., vol. 5, no. 3, pp. 277–285, Sep. 2021, doi: 10.1109/JERM.
2020.3042711.
[12] C. Dachena et al., “Microwave imaging of the neck by means of artificial
neural networks for tumor detection,” IEEE Open J. Antennas Propag.,
vol. 2, pp. 1044–1056, 2021, doi: 10.1109/OJAP.2021.3121177.
[13] M. T. Bevacqua, G. G. Bellizzi, T. Isernia, and L. Crocco, “A method for
effective permittivity and conductivity mapping of biological scenarios
via segmented contrast source inversion,” Prog. Electromagn. Res.,
vol. 164, pp. 1–15, 2019, doi: 10.2528/PIER18071704.
[14] C. Estatico, A. Fedeli, M. Pastorino, A. Randazzo, and E. Tavanti,
“A phaseless microwave imaging approach based on a Lebesgue-space
inversion algorithm,” IEEE Trans. Antennas Propag., vol. 68, no. 12,
pp. 8091–8103, Dec. 2020, doi: 10.1109/TAP.2020.2999789.
[15] X. Li and S. C. Hagness, “A confocal microwave imaging algorithm for
breast cancer detection,” IEEE Microw. Wireless Compon. Lett., vol. 11,
no. 3, pp. 130–132, Mar. 2001, doi: 10.1109/7260.915627.
[16] D. Byrne, M. Sarafianou, and I. J. Craddock, “Compound radar approach
for breast imaging,” IEEE Trans. Biomed. Eng., vol. 64, no. 1, pp. 40–51,
Jan. 2017, doi: 10.1109/TBME.2016.2536703.
[17] M. Li et al., “Machine learning in electromagnetics with applications to
biomedical imaging: A review,” IEEE Antennas Propag. Mag., vol. 63,
no. 3, pp. 39–51, Jun. 2021, doi: 10.1109/MAP.2020.3043469.
[18] Y. Huang, R. Song, K. Xu, X. Ye, C. Li, and X. Chen, “Deep
learning-based inverse scattering with structural similarity loss func-
tions,” IEEE Sensors J., vol. 21, no. 4, pp. 4900–4907, Feb. 2021, doi:
10.1109/JSEN.2020.3030321.
[19] M. Ambrosanio, S. Franceschini, V. Pascazio, and F. Baselice,
“Microwave breast imaging via neural networks for almost real-time
applications,” 2021, arXiv:2103.12522.
[20] A. Al-Saffar, A. Bialkowski, M. Baktashmotlagh, A. Trakic, L. Guo,
and A. Abbosh, “Closing the gap of simulation to reality in electro-
magnetic imaging of brain strokes via deep neural networks,” IEEE
Trans. Comput. Imag., vol. 7, pp. 13–21, 2021, doi: 10.1109/TCI.
2020.3041092.
[21] K. Edwards et al., “Stored grain inventory management using neural-
network-based parametric electromagnetic inversion,” IEEE Access,
vol. 8, pp. 207182–207192 , 2020, doi: 10.1109/ACCESS.2020.3038312.
[22] L. Zhang, K. Xu, R. Song, X. Ye, G. Wang, and X. Chen, “Learning-
based quantitative microwave imaging with a hybrid input scheme,”
IEEE Sensors J., vol. 20, no. 24, pp. 15007–15013, Dec. 2020, doi:
10.1109/JSEN.2020.3012177.
[23] K. Xu, C. Zhang, X. Ye, and R. Song, “Fast full-wave electromagnetic
inverse scattering based on scalable cascaded convolutional neural
networks,” IEEE Trans. Geosci. Remote Sens., vol. 60, pp. 1–11, 2022,
doi: 10.1109/TGRS.2021.3093100.
[24] Z. Lin et al., “Low-frequency data prediction with iterative learn-
ing for highly nonlinear inverse scattering problems,” IEEE Trans.
Microw. Theory Techn., vol. 69, no. 10, pp. 4366–4376, Oct. 2021, doi:
10.1109/TMTT.2021.3098769.
[25] R. Song, Y. Huang, K. Xu, X. Ye, C. Li, and X. Chen, “Elec-
tromagnetic inverse scattering with perceptual generative adversarial
networks,” IEEE Trans. Comput. Imag., vol. 7, pp. 689–699, 2021, doi:
10.1109/TCI.2021.3093793.
[26] L. Xiao, J. Li, F. Han, W. Shao, and Q. H. Liu, “Dual-module
NMM-IEM machine learning for fast electromagnetic inversion of
inhomogeneous scatterers with high contrasts and large electrical dimen-
sions,” IEEE Trans. Antennas Propag., vol. 68, no. 8, pp. 6245–6255,
Aug. 2020, doi: 10.1109/TAP.2020.2990222.
[27] L. Li, L. G. Wang, F. L. Teixeira, C. Liu, A. Nehorai, and
T. J. Cui, “DeepNIS: Deep neural network for nonlinear electromagnetic
inverse scattering,” IEEE Trans. Antennas Propag., vol. 67, no. 3,
pp. 1819–1825, Mar. 2019, doi: 10.1109/TAP.2018.2885437.
[28] Z. Wei and X. Chen, “Deep-learning schemes for full-wave nonlinear
inverse scattering problems,” IEEE Trans. Geosci. Remote Sens., vol. 57,
no. 4, pp. 1849–1860, Apr. 2019, doi: 10.1109/TGRS.2018.2869221.
[29] D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,”
2014, arXiv:1412.6980.
[30] J. Richmond, “Scattering by a dielectric cylinder of arbitrary cross
section shape,” IEEE Trans. Antennas Propag., vol. AP-13, no. 3,
pp. 334–341, May 1965, doi: 10.1109/TAP.1965.1138427.
[31] M. Ostadrahimi et al., “Analysis of incident field modeling and inci-
dent/scattered field calibration techniques in microwave tomography,”
IEEE Antennas Wireless Propag. Lett., vol. 10, pp. 900–903, 2011, doi:
10.1109/LAWP.2011.2166849.
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