microwave imaging through a mode-matching bessel functions procedure

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 61, NO. 8, AUGUST 2013 2753

Microwave Imaging Through a Mode-MatchingBessel Functions Procedure

Navid Ghavami, Gianluigi Tiberi, David J. Edwards, and Agostino Monorchio, Fellow, IEEE

Abstract—A novel imaging procedure based on ultra-widebandmicrowave signals is presented. The procedure exploits the use ofBessel functions mode-matching approach for the identification ofthe presence and location of significant scatterers inside cylindri-cally shaped objects. Simulations and measurements on cylinderswith inclusions are provided to show the capability of the proce-dure for capturing the contrast due to different material proper-ties, and this is achieved through the generation/inversion of rel-atively small matrices. An example involving multilayered cylin-drical objects approximating humanlike tissues containing an in-clusion is also presented.

Index Terms—Microwave imaging, mode matching (MM).

I. INTRODUCTION

M ICROWAVE imaging has attractedmuch interest duringthe last decade, especially for its applicability to breast

cancer detection, motivated by the differing dielectric proper-ties at microwave frequencies of normal and malignant tissues.Current microwave imaging research can be dividedmainly intotomography, ultra-wideband (UWB) radar techniques, and mi-crowave holography.Tomographic image reconstruction techniques are aimed at

recovering an image of the dielectric properties by solving anonlinear inverse scattering problem [1], [2]. Such nonlinear(and ill posed) problems can be addressed by resorting to anumber of methods, including conventional conjugate gradientmethods and the modified Born iterative method [2]. More re-cently, a novel analytical approach (partly derived from pre-vious work [3]) has been introduced by reformulating the in-verse scattering problem as an inverse source one [4], [5].In contrast to tomography, UWB radar approaches address

simpler computational problems since they are focused on iden-tifying and locating the significant scatterers inside a given re-gion [6]–[9]. In order to reconstruct the image, beamformingtechniques of varying complexity and appropriate filters are re-quired. Time-reversal (TR) based approaches have also been

Manuscript received March 26, 2013; accepted May 30, 2013. Date of pub-lication July 12, 2013; date of current version August 02, 2013. This work wassupported by a Marie Curie Intra European Fellowship under the 7th EuropeanCommunity Framework Programme. This work was supported in part by theU.K. Engineering and Physical Sciences Research Council.N. Ghavami and D. J. Edwards are with the Department of Engineering Sci-

ence, University of Oxford, Oxford OX1 2JD, U.K. (e-mail: [email protected]; [email protected]).G. Tiberi is with Fondazione Imago7, Pisa 56126, Italy (e-mail: g.tiberi@iet.

unipi.it).A. Monorchio is with the Department of Information Engineering, University

of Pisa, Pisa 56126, Italy (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMTT.2013.2271612

Fig. 1. Pictorial view of the problem, with the red (in online version) and blackdots representing the receiving and transmitting positions, respectively.

proposed in [10] and [11]. However, TR requires an approxi-mate knowledge of the channel transfer function associated withthe numerical back propagation.In microwave holography, targets in the near-field range are

reconstructed by using a Fourier analysis of the wideband trans-mission and reflection signals recorded by antennas scanningtogether on both sides of the inspected region [12].Presented here is a new method for the imaging of cylindri-

cally shaped objects. The method is based on a mode-matching(MM) procedure of Bessel functions, and it enables the pres-ence and location of significant scatterers within an illuminatedvolume to be identified. It will be shown that the application ofthe MM procedure leads to the generation/inversion of a rathersmall matrix. Simulations and measurements on a cylinderwith one and two inclusions will be provided for methodologyvalidation. Concerning the two inclusion problem, it will beshown that two scatterers can be clearly detected with differentintensities. Specifically, the scatterer with the higher intensitycorresponds to the inclusion with greater mismatch boundaries:thus, the MM Bessel function procedure can discriminateamong multiple scatterers. Finally, an example involving mul-tilayered cylindrical objects constituted of human-like tissuescontaining an inclusion is also presented. Due to the cylindricalnature of the expansion functions, the proposed procedure canbe applied to strictly 2-D problems.

II. MM BESSEL FUNCTION BASED PROCEDURE

Let us suppose we have a cylinder of radius in free space.The cylinder is illuminated by a transmitting line source ,which operates at a frequency . We assume that both the di-electric constant and the conductivity of the cylinderare known. The cylinder is expected to contain an inclusion, asshown in Fig. 1; such an inclusion is assumed to be cylindricallyshaped and with a higher dielectric constant than . Our goalis to identify the presence and location of the inclusion by usingonly the electric field measured outside the cylinder.

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2754 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 61, NO. 8, AUGUST 2013

Let us assume that the field at the surface pointsis known, i.e.,

with (1)

By recalling the cylindrical nature of the problem, the fieldwithin the cylinder can be represented as a summation of Besselfunctions, i.e., a summation of modes

(2)

In (2), is the wavenumber for the media constitutingthe cylinder; moreover, designates the “reconstructed”internal field, while recalls that an MM procedure is em-ployed. It also has to be pointed out that the reconstructed fieldsdepend on the illuminating source and the frequency (since

depends on these parameters). The summation in (2)contains an infinite number of terms: to render the problemmanageable, the summation needs to be truncated afterterms, where has to determined. If , theweights can be calculated by following a least mean square(LMS) approach. To this end, we write the matrix equation

, where

(3a)

(3b)

(3c)

The coefficient vector can be calculated by minimizing theresiduum

(4)

It can be shown that it follows:

(5)

Having determined the weights , the reconstructed field is cal-culated in the entire internal region through (2): such a recon-structed field matches the field observed on the surface points

. It is worth pointing out that the number has to be setlarge enough to allow an accurate reconstruction of the field, butavoiding the matrix to become badly scaled (singular).Other authors have used expansion into functional series to

reduce the ill-posed nature of the inverse problem [13], [14]. In[13], an iterative algorithm is adopted to achieve the solution,leading to an increasing of the CPU time. In [14], the number ofiterations is reduced by exploiting the adjoint variable method.

A. Cylinder Without an Inclusion

Some numerical examples are now provided to show the ca-pability of (2) to represent the internal field. As the first ex-ample, a homogeneous cylinder, i.e., without any inclusion, is

assumed. The cylinder has radius cm, dielectric constant, and conductivity . A transmitting line source

with amplitude equal to 0.001 A and positioned atcm illuminates the cylinder. The frequency of

operation is GHz. The field is calculated atequally phi-spaced points lying on the external sur-

face of the cylinder, and these values are used to fill the vector. Note that the number implies a spatial sampling of

approximately with denoting the wavelength in thecylinder. Moreover, it is worthwhile to point out that, in the ex-amples presented in this section, has been determinedanalytically, while in realistic situations, it will be determinedthrough measurements. Next, the matrix is calculated em-ploying . Finally, the weights are computed byrecalling (5) and the internal field is reconstructed.Note the value has been set after a check on the

convergence of the solution (performed by evaluating the rela-tive error on the magnitude of the reconstructed field). The samevalue is employed in all the examples given in thispaper. We stress again that the dimensions of the matrix arerather small since they are equal to : moreover,in contrast to other inverse techniques, they are not related to thediscretization of the volume where the image is required.In Fig. 2(a), the linear magnitude of the reconstructed internal

field is plotted, while Fig. 2(b) refers to the reference solution,which has been obtained by using the analytical calculation forthe entire internal region. By comparing Fig. 2(a) and (b), it ispossible to note that MM Bessel functions procedure permits toaccurately reconstruct the internal field of homogeneous cylin-ders.

B. Mismatch Boundary Detection and Image Reconstruction

Next, a cylinder with an inclusion is considered. Specifically,a 5-mm radius perfect electrically conducting (PEC) cylin-drical inclusion is concentrically positioned inside the cylinderdescribed in Section II-A. The cylinder is illuminated by thesame line source as in the previous case and the field at

points lying on the external surface is calculated;next, the MM Bessel functions procedure is employed to recon-struct the internal field. Fig. 3(a) shows the linear magnitudeof the reconstructed internal field, while Fig. 3(b) refers to thereference solution, which has been obtained by using the ana-lytical calculation for the entire internal region. By comparingFig. 3(a) and (b), it is possible to note that the internal field isreconstructed quite well everywhere except “near” and “inside”the inclusion. This is due to the difference in properties betweenthe two media, which is not taken into account by (2). More-over, a mismatch in the region of transition of the two mediais clearly visible in the reconstructed field, paving the way fora new strategy for detection and localization. Considering theproblem in more detail, suppose the external cylinder is illu-minated using a range of different frequencies and from manylocations; all the reconstructed fields will exhibit the mismatch,which will be always located in the region of transition of thetwo media. It follows that if we sum all the solutions, i.e., thereconstructed fields, in an incoherent fashion, the inclusionwill be detected and localized. Mathematically speaking, if weemploy transmitting sources with ,

GHAVAMI et al.: MICROWAVE IMAGING THROUGH MM BESSEL FUNCTIONS PROCEDURE 2755

Fig. 2. Magnitude (linear) of the field of a homogeneous cylinder illuminatedby a line source: reference (b) and reconstructed (a) field obtained through theMM-Bessel function procedure; - and -axes are in meters.

and frequencies with , it follows that theintensity of the final image can be expressed as

(6)

The resolution is expected to reach the optical resolution limitof , where denotes the wavelength in thecylinder calculated at the highest frequency; this feature can beused as a rule of thumb for determining the highest frequencyto be employed in the procedure.

C. Numerical Results and Methodology Characterization

The proposed method is now validated through a numericalexample. Specifically, we assume a cylinder with radiuscm, dielectric constant , and conductivity .

The cylinder has one cylindrically shaped inclusion with radius

Fig. 3. Magnitude (linear) of the field of cylinder with PEC intrusion illumi-nated by a line source: reference (b) and reconstructed (a) field obtained throughthe MM-Bessel function procedure; - and -axes are in meters.

mm, dielectric constant , and conductivity. The inclusion is placed eccentrically at a distance of

1 cm from the center of the cylinder (please refer to Fig. 4 formore details).

transmitting line sources (with) illuminate the cylinder; these transmitting line

sources are located at a distance of 8 cm from the center and areequally spaced along phi. The band of 8–10 GHz is used, witha frequency sampling of 10 MHz. For each transmitting linesource and for each frequency sample, the field atpoints lying on the external surface, , is calculated;next, the MM Bessel functions procedure is employed to re-construct the internal field. It is worthwhile to point out that,in this example, has been determined analytically byresorting to [15]. Fig. 5(a)–(c) shows the linear magnitudeof the reconstructed fields for a given frequency sample anddifferent illuminating sources; the figures highlight the above,


Fig. 4. Pictorial view of the problem: multi-sources illumination.

i.e., that all the reconstructed fields exhibit the mismatch, whichis always located in the region of transition of the two media.In Fig. 6, the normalized intensity (linear) calculated through

(6) is depicted; a peak can be clearly detected in the region of theinclusion, which has been marked with a white circle. It followsthat both detection and localization are achieved [16]. From thefigure, it can be stated that the resolution (which can be definedas the dimension of the region whose normalized intensity isabove 0.5) is approximately 2.5 mm; this value is in agreementwith the optical resolution limit of . Concerning thesignal to clutter ratio (S/C), here defined as the quantity thatcompares the maximum inclusion response with the maximumclutter response in the same image, a value of 7 dB is achieved.Note that dB has been obtained with trans-mitter positions and 2 GHz of bandwidth; it can be shown thata lower number of transmitting positions leads to a lower S/C,while an increase of the bandwidth leads to a higher S/C (moredetails can be found in [9]).The values of were chosen in accordance with [6]–[9]

to more nearly reproduce the normal and malignant breast tissueproperties in the band of interest. It is worthwhile to point outthat in [6]–[9] the contrast between malignant tissue and healthybreast tissue is assumed to be quite significant (i.e., equal orgreater than a factor of 5 in permittivity and conductivity). How-ever, more recent studies indicate that such contrast exists be-tween malignant and fatty (or adipose) breast tissue, while thecontrast between malignant and healthy fibroglandular tissuescan be as low as 10% in both permittivity and conductivity [17].

III. CYLINDER WITH MULTI-INCLUSIONS:MEASUREMENTS AND SIMULATION

The capability of the MM Bessel function procedure to de-tect and locate inclusions has been verified through measure-ments. A cylinder with a single inclusion has been investigatedin [18]. Here, to assess the applicability of MM in solving com-plex problems, a medium with two inclusions was considered.Specifically, a Polymethylmethacrylate (Perspex or Plexiglass)(P.M.M.A) cylinder with a radius of 4.25 cm and a height of30 cm was constructed. The dielectric constant and the con-ductivity of the P.M.M.A cylinder are and

S/m. The cylinder contains an inclusion consisting ofa perfect electric conductor (PEC) 3-mm radius cylinder; thisinclusion is eccentrically placed at a distance of 2 cm from the

Fig. 5. Magnitude (linear) of the field of cylinder with inclusion illuminated bya line source: reconstructed field obtained through the MM-Bessel function pro-cedure when considering GHz and: (a) , (b)

, and (c) ; - and -axes are in meters.

center of the cylinder. In addition, a second inclusion was ef-fected by drilling a 3-mm radius hole at a distance of 2 cm


Fig. 6. Normalized intensity (linear) obtained by adding all the reconstructedfields obtained through (6); the white circle indicates the position of the inclu-sion; - and -axes are in meters.

Fig. 7. Cast P.M.M.A cylinder having a radius of 4.25 cm with PEC andagar–agar solution inclusions.

from the center of the cylinder and at 90 (relative to center)from the PEC inclusion (please refer to Fig. 7 for more details).The drilled cavity was then filled with an agar–agar solution.Agar–agar gels are often used for approximating high-water-content human tissues. From [19], both the dielectric constantand the conductivity are functions of the concentration of theagar–agar; a concentration of 6% has been used in this exper-iment, leading to S/m. Agar–agar was dis-solved in water at approximately 95 C and then cooled to roomtemperature.A vector network analyzer (VNA) arrangement in an ane-

choic chamber has been utilized to measure the transfer func-tion at 1601 discrete frequencies in the band of 6–10 GHz.Wideband bow-tie antennas, vertically polarized and omni-di-rectional in the azimuth plane, were used (after checking that

is lower than 10 dB in the band of interest). For eachset of measurements, the location of the transmitting antenna

Fig. 8. Normalized intensity obtained through (6) when using the castP.M.M.A cylinder having a radius of 4.25 cm with PEC and agar–agar solutioninclusions.

was fixed at approximately 20 cm away from the center of thecylinder, while the receiver antenna was positioned close to theexternal surface of the cylinder and placed on a computer-con-trolled rotating stage with 3° of angular resolution. Thus, thefield at equally phi-spaced points lying onthe external surface were measured; note that leadsto spatial sampling, where represents thewavelength in the P.M.M.A cylinder computed at the highestfrequency. We recorded a total number of sets of data(with ), changing the position of the transmit-ting antenna for each set along phi with a step of 60°. Fig. 8shows the normalized intensity (linear) obtained through (6)after a proper image adjusting (consisting in enforcing to zerothe values below 0.25 and expanding from 0 to 1 the valuesabove 0.25). From the figure, it is possible to clearly detect twopeaks positioned in the region of the inclusions, and having dif-ferent intensities. Specifically, the peak with the higher intensitycorresponds to the PEC inclusion (due to the fact a greater con-trast, i.e., greater mismatch boundaries, occurs when going fromP.M.M.A to the PEC cylinder), while the less intense peak rep-resents the location of the agar–agar solution inclusion. Hence,both detection and localization are achieved, showing the abilityof the MM Bessel function procedure in resolving and correctlydiscriminating among multiple scatterers. This latter feature isof fundamental importance since it paves the way for addressingproblems also involving tissues inhomogeneities.If a full automatic scanning system is used, the 6 120 mea-

surements can be collected in approximately 12 min; a furtherreduction can be achieved if employing a receiving array config-uration. The number of receiving position could be slightlyreduced, but the condition must be alwaysverified.The P.M.M.A cylinder with the two inclusions has also been

analyzed through simulations. Specifically, the measurementsdescribed above have been reproduced through the proceduregiven in Section II-C: first, has been determined ana-lytically by resorting to [15]; next, the image has been derived


Fig. 9. Normalized intensity obtained through (6) when analyzing throughsimulations the P.M.M.A cylinder having a radius of 4.25 cm with PEC andagar–agar solution inclusions.

through (6). Fig. 9 shows the normalized intensity (linear) ob-tained after an image adjusting process (consisting of enforcingto zero the values below 0.25 and expanding from 0 to 1 thevalues above 0.25). Two peaks can be clearly detected in the re-gion of the inclusions with different intensities, confirming theresults of Fig. 8.

IV. MULTI-LAYERED CYLINDER WITHINCLUSION: MEASUREMENTS

To access the ability of the MM method in locating an inclu-sion in multi-layered problems, a multi-layered cylinder havinga human tissues characteristic was constructed. To achieve thispurpose, a PVC cylindrical pipe with a radius of 5 cm was con-centrically placed inside a larger plastic pipe with a radius of6.25 cm.Both pipes were filled with agar–agar gel approximating to

a high water-content human tissue; a 3-mm-thick PEC rod waspositioned eccentrically inside the gel, at a distance of 3.25 cmfrom the center of the cylinders (Fig. 10). For this experimenttwo distinct concentrations of agar were used, i.e., 6% for theexternal layer and 8% for the internal one. Moreover, somesalt was added to the internal layer agar mixture. The dielec-tric constant of the external layer was calculated to be equal to70, while the dielectric constant of the internal layer showedan increase of approximately 5% [19]. The conductivity of theexternal layer was calculated to be 1 S/m, while the conduc-tivity of the internal layer showed an increase of approximately50%, due to the salt [19]. It follows that the experiment rep-resents the case of having two layers with a slight differencein dielectric constant and a difference of 50% in conductivity.Frequency-domain UWBmeasurements were performed in freespace using a VNA arrangement to obtain the transfer function.Discone antennas, vertically polarized and omni-directional inthe azimuth plane, were used after calibration. The measure-ments were recorded at 1601 discrete frequencies in the band of2–6GHz (after checking that the is lower than 10 dB in theband of interest). For each set of measurements, the location of

Fig. 10. Multilayered cylinder with an inclusion. A PVC cylindrical pipe withradius of 5 cmwas concentrically placed inside a larger plastic pipe with a radiusof 6.25 cm. Both pipes were filled with agar–agar gel: two distinct concentra-tions of agar were used, i.e., 6% for the external layer and 8% for the internalone. Moreover, some salt has been added to the internal layer agar mixture. Theinclusion is represented by a PEC rod positioned eccentrically at a distance of3.25 cm from the center of the cylinders.

Fig. 11. Normalized intensity obtained through (6) when using the multilay-ered cylinder with an inclusion.

the transmitting antenna was fixed approximately 15 cm awayfrom the axis of the cylinder, while the receiver antenna was po-sitioned close to the external surface of the agar–agar cylinderand mounted on a computer controlled rotating stage with 3°of angular resolution. Thus, the field atequally phi-spaced points were measured. A total number of

sets of data were recorded (with ),changing the position of the transmitting antenna along phiwitha step of 90°; Fig. 11 shows the normalized intensity (linear)obtained through (6) after the previously described image ad-justing process. Again, a peak can be clearly detected in the re-gion of the inclusion. It follows that the proposed MM can be


applied for detecting inclusion in multi-layered structure: obvi-ously this holds true when the layers have a slight difference indielectric constant (5% in this example). In Fig. 11, some ghostimages having normalized intensity up to 0.4 can be noted; theseimages can be presumably related to reflections from interfaceof the PVC cylinder used to realize the phantom.

V. CONCLUSION

It has been shown that, if the properties of the external objectare known, the MM Bessel function procedure permits the de-tection of the presence and location of significant scatterers in-side cylinders. Simulations and measurements on cylinder withone and two inclusions have been provided for methodologyvalidation. Concerning the two inclusion problem, it has beenshown that two peaks can be clearly detected, with differentintensities. Specifically, the peak with the higher intensity cor-responds to the inclusion with greater mismatch boundaries.Hence, both detection and localization are achieved, showingthe ability of the MM Bessel function procedure in resolvingand discriminating among multiple scatterers.An example involving multilayered cylindrical objects con-

stituting of human-like tissues containing an inclusion has alsobeen successfully presented.The achievable resolution (which can be defined as the

dimension of the region whose normalized intensity is above0.5) is one-quarter of the shortest wavelength in the dielectricmedium. Concerning the S/C ratio, here defined as the quantitythat compares the maximum inclusion response with the max-imum clutter response in the same image, a value of 7 dB hasbeen achieved when employing transmitter positionsand 2 GHz of bandwidth.The MM Bessel function procedure requires the genera-

tion/inversion of small matrices; specifically, the dimensionsare equal to and they are not related to thediscretization of the volume where the image is required.The use of Bessel functions seems to limit the applicability

to 2-D cylindrically shaped objects. One can think to replaceBessel functions with Mathieu functions or spherical Besselfunctions if ellipsoidal and spherical problems are encountered.An extension to more realistic 3-D geometries is possible byusing the extraction of the modes. Specifically, the modes area set of basis functions that are necessary and sufficient for therepresentation of the electromagnetic field inside the object (ata given frequency); the modes can be numerically evaluated byresorting to the characteristic basis function method (CBFM)[20], [21]. Research is in progress to assess this point.

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Navid Ghavami received the B.Eng degree inelectrical and electronic engineering (with first-classhonors) from King’s College London, London, U.K.,in 2009, and the Ph.D. degree from the University ofOxford, Oxford, U.K., in 2013.He is currently a Post-Doctoral Research Assistant

with the Department of Engineering Science, OxfordUniversity. His research interests include medicalimaging and ultra-wideband communications.Dr. Ghavami was the recipient of secen university-

wide prizes including an IEEE prize for Best FinalYear Project in the field of telecommunications.


Gianluigi Tiberi received the Laurea degree intelecommunication engineering and Ph.D. degreefrom the University of Pisa, Pisa, Italy, in 2000 and2004, respectively.In 2000, he was a Visiting Researcher with the

Centre for Telecommunication Research, King’sCollege London, London, U.K. From September toDecember 2002, he was a Visiting Ph.D. Researcherwith the Electromagnetic Communication Labora-tory, Pennsylvania State University, University Park,PA, USA.

In 2004, he joined the Microwave and Radiation Laboratory, Department ofInformation Engineering, University of Pisa, as a Post-Doctoral Researcher.FromMarch 2009 to March 2010, he spent one year with the Department of En-gineering Science, University of Oxford. He currently conducts research withFondazione Imago7, Pisa, Italy, where he coordinates the Radio Frequency Lab-oratory of the first 7.0 T Magnetic Resonance (MR) center in Italy. His re-search interests include high-frequency-derived approaches for solving elec-tromagnetic scattering problems, electromagnetic propagation in complex en-vironments, wideband/UWB channel modeling, and microwave and magneticresonant imaging for medical application.Dr. Tiberi (jointly with the Department of Engineering Science, University

of Oxford) was the recipient of Marie Curie Intra European fellowships for Ca-reer Development, Seventh Research Framework Programme (FP7-PEOPLE-2007-2-1-IEF).

David J. Edwards received the B.Sc, M.Sc, andPh.D. degrees in physics and the physics of materialsand engineering from the University of Bristol,Bristol, U.K.He is currently a Professor of engineering science

and Sub-Warden and Fellow with Wadham CollegeOxford, University of Oxford, Oxford, U.K. After 12years spent in industry (British Telecom), he returnedto academia and has been an academic for 28 years(four years with Bristol University and 24 years withOxford University). He has acted as a consultant to

a large number of industrial organizations during his career. He has authoredor coauthored over 300 publications during his time as an academic and hasbeen extremely well supported by funding from research councils and industryand government agencies. He holds numerous patents, with several appearingas licensed commercial products. His current research interests include commu-nications, antennas and propagation, electromagnetics, ad hoc networks, mul-

tiple-input multiple-output (MIMO) systems, materials for electromagnetic ap-plications, radio astronomy technology, and medical imaging.Prof. Edwards is a Chartered Engineer. He is a Fellow of the Institution of

Engineering and Technology (IET) and the Royal Astronomical Society. Hehas served on a number of national and international committees relating to theantennas and propagation fields. He has been the receipt of a number of awardsand prizes in recognition of his work and has a strong record of innovation incommunications systems, techniques, and technologies.

Agostino Monorchio (S’89–M’96–SM’04–F’12)received the Laurea degree in electronics engineeringand Ph.D. degree in methods and technologies forenvironmental monitoring from the University ofPisa, Pisa, Italy, in 1991 and 1994, respectively.During 1995, he joined the Radio Astronomy

Group, Arcetri Astrophysical Observatory, Florence,Italy, as a Postdoctoral Research Fellow, wherehe was involved in the area of antennas and mi-crowave systems. He has been collaborating withthe Electromagnetic Communication Laboratory,

Pennsylvania State University, University Park, PA, USA, and is an Affiliate ofthe Computational Electromagnetics and Antennas Research Laboratory. Hehas been a Visiting Scientist with the University of Granada, Granada, Spain,and with the Communication University of China, Beijing, China. In 2010, hewas affiliated with the Pisa Section of the National Institute of Nuclear Physics(INFN). He is currently an Associate Professor with the School of Engineering,University of Pisa, and an Adjunct Professor with the Italian Naval Academy ofLivorno, Livorno, Italy. He is also an Adjunct Professor with the Departmentof Electrical Engineering, Pennsylvania State University. He is on the TeachingBoard of the Ph.D. course in “Remote Sensing” and on the council of thePh.D. School of Engineering “Leonardo da Vinci,” University of Pisa. Hehas been a reviewer for many scientific journals and has been supervisednumerous research projects related to applied electromagnetics, commissionedand supported by national companies and public institutions. He is activein a number of areas, including computational electromagnetics, microwavemetamaterials, antennas and radio propagation for wireless networks, activeantennas, and electromagnetic compatibility.Dr. Monorchio has served as an associate editor for the IEEE ANTENNAS AND

WIRELESS PROPAGATION LETTERS. He was the recipient of a Summa Founda-tion Fellowship and a North Atlantic Treaty Organization (NATO) Senior Fel-lowship.

microwave imaging through a mode-matching bessel functions procedure

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