426 IEEE SENSORS JOURNAL, VOL. 7, NO. 3, MARCH 2007

A Multimodal Tomography SystemBased on ECT Sensors

Qussai Marashdeh, Member, IEEE, Warsito Warsito, Member, IEEE, Liang-Shih Fan, andFernando L. Teixeira, Senior Member, IEEE

Abstract—A new noninvasive system for multimodal electricaltomography based on electrical capacitance tomography (ECT)sensor hardware is proposed. Quasistatic electromagnetic fieldsare produced by ECT sensors and used for interrogating thesensing domain. The new system is noninvasive and based oncapacitance measurements for permittivity and power balancemeasurements for conductivity (impedance) imaging. A dual sen-sitivity map of perturbations in permittivity and conductivity isconstructed. The measured data along with the sensitivity matrixare used for the actual image reconstruction. The new multimodaltomography system has the advantage of using already establishedreconstruction techniques, and the potential for combination withnew reconstruction techniques by taking advantage of combinedconductivity/permittivity data. Moreover, it does not require directcontact between the sensor and the region of interest. The systemperformance has been tested on representative data, producinggood results.

Index Terms—Electrical capacitance sensor, impedance tomog-raphy, iterative reconstruction, quasi-static fields.

I. INTRODUCTION

I NDUSTRIAL flow processes tend to be complex in nature,and often involve a variety of components in a combination

of gas, liquid, and solid phases. Process (flow) tomography hasprovided a leap forward in real-time flow estimation for im-proved industrial process monitoring and control [1], [2]. Imple-mentation of process tomography have been achieved througha variety of techniques. The most conspicuous techniques arethose based on measurement of electrical properties, through theutilization of capacitive, conductive, or inductive nature of theflow components under investigation. In most cases, electricaltomography is implemented based on measurements of a single

Manuscript received January 9, 2006; accepted September 26, 2006. Thework was supported in part by the National Science Foundation under GrantCTS-0207068 and in part by a SPWLA fellowship. The associate editor coordi-nating the review of this paper and approving it for publication was Prof. RalphEtienne-Cummings.

Q. Marashdeh is with the Department of Electrical and Computer Engi-neering and the Electroscience Laboratory and the Department of Chemicaland Biomolecular Engineering, The Ohio State University, Columbus, OH43210 USA (e-mail: marashdeh.1@osu.edu).

W. Warsito and L.-S. Fan are with the Department of Chemical and Biomelu-cular Engineering, The Ohio State University, Columbus, OH 43210 USA(e-mail: wsito@yahoo.com; fan.1@osu.edu).

F. L. Teixeira is with the Department of Electrical and Computer Engineeringand the Electroscience Laboratory, The Ohio State University, Columbus, OH43210 USA (e-mail: teixeira@ece.osu.edu).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSEN.2006.890149

constitutive property, viz., permittivity for electrical capacitancetomography (ECT), or conductivity for impedance (resistivity)tomography. However, the need for real-time imaging of com-plex processes involving multiphase components has motivatedin recent years the development of imaging systems exploitingmultiple electrical properties [3], i.e., multimodal tomography.

Multimodal tomography is, in general, implemented throughthree different strategies [4]: 1) integration of two or moresensor tomography hardware components into one imagingsystem (e.g., gamma-ray and ECT tomography [5]); 2) the useof reconstruction techniques capable of differentiating betweendifferent components and phases based on a single sensingsignal (e.g., multicriteria reconstruction techniques [4]); and3) the use of single sensor hardware to acquire different signalscorresponding to different electrical properties (e.g., impedancetomography sensors for imaging permittivity and conductivity[6]). Although the first strategy is fast, it has a disadvantage interms of its high cost and instrumentation complexity (addedhardware). In addition, the data acquisition needs to be carefullycoordinated for real-time applications to yield consistent data atdifferent time frames. The second strategy is the least costly toimplement. However, it yields relatively longer reconstructiontimes due to more involved reconstruction algorithms. The thirdstrategy is inherently multimodal since it provides all requiredinformation (on different electrical properties) using the samesensor hardware and same reconstruction technique. Moreover,integration of such systems with multimodal reconstructiontechniques can provide independent data for different phasesin the imaging domain. For example, obtaining both capacitiveand conductive (impedance) flow information simultaneouslyis beneficial in many applications [6], particularly when theflow under consideration is a mixture of components withwidely different conductivity and permittivity constants suchas oil-gas-water flow along a pipeline.

Electrical impedance tomography (EIT) has been extensivelyused for both medical and industrial applications [7]. AlthoughEIT commonly refers to (unimodal) resistivity tomography sys-tems, it can also be used for permittivity/conductivity imagingby considering amplitude and phase measurements of the inter-rogating signal. However, such applications depend on currentinjection [8], which requires direct contact between the sensorand imaging domain. This is not viable when an insulating el-ement separates the flow of interest from the sensor system it-self, as in many industrial processes. In this case, one commonrequirement for the tomographic system is to be both noninva-sive (i.e., not in direct contact with the domain of interest) andnonintrusive (i.e., not to affect the process under examination)[2].

1530-437X/$25.00 © 2007 IEEE

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Fig. 1. Cross section of ECT sensor consisting of 12 electrodes surrounding acylindrical vessel.

In this work, a new noninvasive multimodal tomographysystem is proposed based on the use of ECT sensor hardware.Unlike usual ECT sensor operation which assumes a staticinterrogating field, the interrogating field of the proposedsystem operates under quasi-static conditions. The ECT sensorsystem is employed to simultaneously measure variations inboth capacitance and power corresponding to permittivity andconductivity distributions, respectively, within the sensingdomain (vessel). A dual capacitance/power sensitivity matrixis obtained and used in approximate image reconstructionalgorithm based on iterative linear back projection (ILBP).The system performance is tested on different permittivity andconductivity flow distributions, showing very good results.

II. ECT SENSOR DATA ACQUISITION

A. ECT Sensors

ECT sensors, such as those depicted in Fig. 1, are usuallynoninvasive and nonintrusive. An ECT sensor generally consistsof electrodes placed around the region of interest, providing

independent mutual capacitance measurements. Ina typical ECT system, the frequency of the excitation signal isabout 1–10 MHz [6], and the sensor size is less than few metersin either dimension. As a result, the wavelength is much largerthan the size of the sensor and a static or quasi-static approx-imation can be employed to describe the field behavior. ECTanalysis in the literature is carried out by assuming a static ap-proximation for the electric field distribution (modulated by thetime variation).

In situations related to time varying fields, the electric andmagnetic fields at the observation point change values sometime after a change at the source. The time (propagation) delaydepends on the distance between source and observation pointsand on the intervening media. In cases where the physical di-mensions of the problem are significantly smaller than the wave-length of the excitation, this propagation delay can be neglectedand static laws can be applied to time varying fields [9]. Ap-plying a quasi-static approximation in Maxwell’s equations, theelectric field distribution obeys the following equation:

(1)

where is the electric potential, is the electricfield intensity, is the angular frequency, is the conduc-tivity, is the permittivity, and is the position vector.

The mutual capacitance between any two pair of elec-trodes and (source and detector) is given by

(2)

where is the potential difference, is a closed surface (orpath in 2-D) enclosing the detecting electrode, and is the unitnormal vector to . Moreover, the r.m.s. power dissipated by aconductive object in the domain of interest, given the potentialdistribution due to the source electrode at voltage anddetector electrode at ground voltage is given by

(3)

Equations (2) and (3) relate the permittivity and conductivitydistributions to (global) measurements of capacitance andpower, respectively. The solution for and givenand constitutes the forward problem. The process ofobtaining and from capacitance and power measure-ments constitutes the inverse problem.

B. Data Acquisition

In conventional ECT acquisition systems, the hardware isrealized based on one of two circuits types: 1) charge dischargecircuit, and 2) AC-based circuit [10]. In both strategies, thecurrent produced from the excitation signal is converted intoa voltage signal through an operational amplifier (OP-AMP).Extending the measurement circuit to extract power valueswould require a modification to the ECT acquisition system.Two strategies are proposed in this case: 1) current-phase mea-surement, and 2) independent capacitance-power measurement.In the former, the ECT circuit for measuring the current ismodified to include a phase meter of the current with respectto the source voltage. The amplitude of the current along withthe phase value are used in this case to measure the powerconsumption in the circuit. In the latter case, an independentcircuit is connected to the ECT sensor operating on the sameclock of the capacitance circuit. In this case, the capture speedof the entire system would be reduced to half of the speed inthe first method. Note that a dual calibration of capacitanceand power is required for proper measurements. The powercalibration can be conducted similar to capacitance calibrationexplained in this paper.

C. Equivalent Lumped-Circuit Models

It is useful to express field relations in terms of equivalentlumped-circuit models whenever possible [11]. In the presentscenario, equivalent circuit models for each parallel plate pairin the ECT sensor can be constructed as a parallel associationof a lumped resistor and capacitor , representing ohmiclosses and the mutual capacitance, respectively, between eachparallel plate pair of the ECT sensor. These lumped elementsassume different values whether an empty vessel is consideredor an object is present in the imaging domain. In particular, theequivalent resistor would be infinite if the background mediumassociated to an “empty” vessel scenario is lossless. The equiv-alent parameters can be extracted both from measurements and

428 IEEE SENSORS JOURNAL, VOL. 7, NO. 3, MARCH 2007

from field calculations, and then used for the reconstructionprocess, as detailed below.

In terms of the field distribution and the constitutive param-eters, the resistance and the change on can be approx-imated as

(4)

(5)

where the superscript refers to the empty vessel case, and tothe filled (loaded) vessel case.

III. SENSITIVITY MATRIX CALCULATION

Obtaining inverse solutions for and given anddata can be time consuming [12]. The main difficulty for ECTsensors (and for electrical tomography sensors in general) is thesoft-field nature of the problem [13]. In soft-field tomography,the interrogating field (potential) depends on the electric prop-erty distributions and in a nonlinear fashion. Moreover, thereis no analytic solution for the forward problem in general, andaccurate solutions can only be obtained via brute-force com-putational techniques such as finite differences and finite ele-ments [14]. The large computational resources and long com-putational time required make these techniques impractical forfast (real-time) reconstruction and monitoring. A popular ap-proximation strategy used in practice consists on a linearizationof the problem using sensitivity matrix models [15]. The sensi-tivity matrix is built by considering small perturbations (pixels)filled with a material of higher permittivity or conductivity. Theresponse of the sensor for each perturbation is organized in a(sensitivity) matrix according to their location in the sensing do-main to form a basis set for (linear) reconstruction. Moreover,the forward solution in this case is obtained as a superposition ofsensor responses to different perturbations, commonly referredto as linear forward projection (LFP). The sensitivity matrixacts as a forward projection matrix between electric propertydistribution and sensor boundary measurement. The transposeof the sensitivity matrix can be used for back projection. Backprojection techniques are used to solve the inverse problem andinclude variants such as linear back projection (LBP) [15], iter-ative linear back projection (ILBP) [13], pseudoinverse projec-tion [12], and regularized projection [16].

In this paper, a dual sensitivity matrix that includes both ca-pacitance and power measurement data is constructed and usedto solve the forward and inverse problems in an approximatefashion. The dual matrix elements are approximated based onthe electric field distribution in the empty sensor scenario.

A. Capacitance Sensitivity Matrix

An approximate (first-order perturbation) method for sensi-tivity matrix calculation has been introduced in [17] based onapproximating the change in capacitance introduced by a per-turbation using the electric field from an empty sensor. Thechange in capacitance is related directly to the difference in

total stored energy caused by the permittivity pixel. This en-ergy difference is composed of two components [17]: internalto the pixel , andexternal to the pixel , where

is the effective pixel volume, is the pixel permittivity,is the polarizability, is the background permittivity, isthe (unperturbed) electric field amplitude at the pixel location,and is a constant related to the relative permittivity values.Combining these two equations, we have

. In order to obtain the sensitivity matrix, thesensor model has to be solved only once, for the empty case.

The sensitivity matrix is normalized according to the capaci-tances measured for the empty and fully dielectric filled vesselsas

(6)

where represents normalized sensitivity matrix elements,and and are the elements for filled and empty vessels,respectively. In the linear case, this would produce only posi-tive normalized capacitances. In practice, due to nonlinearitiesin the actual problem, negative values for the sensitivity matrixelements can occur. In general, the efficacy of the above lin-earization approach is established based on its integration intoiterative approximate reconstruction algorithms, as detailed inSection V.

B. Power Sensitivity Matrix

Similarly to the capacitance matrix, each element in thepower matrix linearizes the relation between the conductive(heating) loss and a small conductive pixel perturbation in aninsulating background given by (3), integrated over a (small)pixel volume with conductivity .

The electric field is found by solving (1) and using (3) todetermine the dissipated power. We assumed that the per-turbation is a small pixel with uniform conductivity and an(effective) interior field that is approximated as a function ofthe unperturbed (empty vessel) field and a correction factor

to be determined. In this way, (3) is approximatedas . In this approximation, theforward problem needs to be solved once for to determinethe power matrix. However, can vary by many orders ofmagnitude in practice, and depends on the solu-tion of Poisson equation. For (ECT operationfrequency considered), can be approximated at thediffusion regime as forgiven in S/m, and at the displacement regime as

. The diffusion regime refers tothe electron current density (resulting in a conduction current)being dominant, whereas the displacement regime refers to thepolarization charge oscillations of dielectric material (resultingin a displacement current) being dominant. This is illustrated inFigs. 2–4, which show FEM results for the normalized electricfield and associated power loss of a small spherical pixel with10-mm radius placed in a 10-MHz uniform field. The powermatrix is normalized analogously to the capacitance matrix.However, since the the power dissipated in the empty vessel

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Fig. 2. Normalized electric field jE=E j as a function of conductivity � inS/m.

Fig. 3. Normalized electric field jE=E j as a function of relative permittivity� .

case is zero, the power sensitivity matrix elements remainspositive, despite of nonlinearities.

The power matrix approximation above ignores any skineffect or, equivalently, assumes that the skin depth is muchlarger than the diameter of the vessel. This puts a limit on themaximum conductivity to be imaged in the diffusion regime.A decrease on the frequency of operation can increase the skindepth for a given conductivity. However, lower frequenciesproduced lower (power) signals, characterizing a fundamentaltradeoff.

IV. RECONSTRUCTION TECHNIQUE

The soft field nature and ill-posedness of the inverse problemare the main problems encountered in the reconstruction step[18]–[22]. Although more accurate nonlinear inverse problemsolutions have been the subject of intensive research, the mostcommonly applied reconstruction techniques are still based on

Fig. 4. Power dissipation as a function of conductivity� in S/m inside the pixel,for the normalized electric field in Fig. 2.

Fig. 5. Power vectors of forward solutions for the flow distribution depicted atthe bottom right corner. The electrical properties for (ring) zone B are � = 5

and � = 0 S/m , whereas for (central) zone A, � = 5, and � (S/m) varies asindicated by the legend.

(linearized) sensitivity models. In this work, iterative linear backprojection (ILBP) is used. In contrast to traditional ILBP basedon a single modality sensitivity matrix, a dual modality sensi-tivity matrix is employed here, where the first component of thematrix represents the capacitance perturbation and the secondcomponent refers to the conductivity perturbation, as detailedin the Section III.

In ILBP, the image vector is updated iteratively to minimizethe error between measured and calculated data according to

(7)

where the calculated data is obtained from the (last) recon-structed image using linear forward projection. In (7), isthe image vector, is the iteration number, is the sensitivity

430 IEEE SENSORS JOURNAL, VOL. 7, NO. 3, MARCH 2007

Fig. 6. Reconstruction results for the original distribution values depicted on the left (diffusion dominated case). In this figure and the following ones, the permit-tivity indicated refers to relative permittivity and the conductivity is given in S/m. Both reconstruction results are normalized to unity.

Fig. 7. Normalized reconstruction results for the original distribution values depicted on the left (displacement dominated case).

matrix, is a factor controlling the reconstruction convergence,and is the boundary measurement. In the dual modalityreconstruction performed here, and are both complexvectors, with the real part associated with the permittivitydistribution and measured capacitance, respectively, and theimaginary part with conductivity distribution and measureddissipated power, respectively.

Further improvements on the image quality of the ap-proximate ILBP reconstruction are generally implementedthrough applying (postmode) image constraints, regularizationparameters, and/or image processing filters. For example, alimiting constraint of maximum and minimum reconstructedpixel values can be applied to (7) for benefit of the so-calledprojected Landweber iteration [12]. In this work, a thresholdingfilter is applied to the reconstructed images in their postmode.This filter is aimed at removing smooth transitions betweenregions of different electrical property due to blurring causedby ILBP.

Implementing iterative reconstruction techniques requiressolving the forward and inverse problems multiple times. Theuse of sensitivity matrix models in its present form also relieson the assumptions that the field distributions that are not

strongly affected by the permittivity and conductivity pixeldistributions for the complementary measurements, viz., powerand capacitance measurements, respectively. Although thisassumption does not remain valid, in general, it is valid indisplacement dominated and diffusion dominated regimes. Inthe displacement dominated regime, the displacement current isdominant over the conduction current, whereas in the diffusiondominated regime, the conduction current is the one dominant.In both cases, one electrical property is dominant over the otherin determining the measurement perturbation, and reconstruc-tion can be performed independently for the permitttivity andconductivity distributions.

V. RECONSTRUCTION RESULTS AND DISCUSSION

A 10-MHz ECT sensor layout composed of 12 electrodes, asdepicted in Fig. 1, is used to assess the multimodal tomographysystem performance proposed here. Simulations for sensitivitycalculations and boundary measurements are carried out usingFEM, where a dual sensitivity matrix for capacitance and powerperturbations is constructed based on the electric field distribu-tion in the empty sensor state. Boundary measurements of ca-

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Fig. 8. Normalized reconstruction results for the original distribution values depicted on the left (displacement dominated case).

Fig. 9. Normalized reconstruction results for the original distribution depicted on the left. Because of the reduced value of the skin depth at the outer ring zone,the reconstruction fails to reproduce the original distribution.

pacitance and power, as well as sensitivity elements, are nor-malized for image reconstruction according to

(8)

where , are the boundary values (power and capaci-tance) when the vessel domain is entirely filled with low andhigh values of the corresponding electric property (conductivityfor power and permittivity for capacitance), and is the mea-sured data. The reconstruction process and data forward simu-lations were carried out on a Pentium IV computer, with 2-GHzprocessor and a 1-GB RAM memory. The sensing domain is acylindrical vessel with 1 m radius. Inside the sensing domain,various fluid flow distributions are simulated as indicated bythe original distributions in Figs. 6–9. In this case, a cylindricalflow zone with 0.5 m radius (zone ) and a cylindrical ring flowzone with 0.667-m inner radius and 0.95-m outer radius (zone

), with each zone having a different pair and , co-exist.The background medium is set as , . Permittivityvalues refers here to relative permittivity. The corresponding re-construction results using ILBP are shown in the same figures.

In Fig. 5, power measurements for each capacitor plate pairare provided for the flow distribution when relative permittivity

of both zone and zone is 5, and the conductivity values areindicated in the figure. Although the measured dissipated powerchanges with the conductivity, it does not uniquely predicts theconductivity value. This is because the dissipated power maydepend on the permittivity constant as well, as shown in Fig. 4.

As discussed in Section IV, the relative value of conductivitywith respect to permittivity is an important variable for definingthe performance of reconstruction. In Fig. 6, the high value ofconductivity constant in the zone (diffusion dominated) en-ables the solution to converge to two distinct regions of permit-tivity and conductivity maps. In Fig. 7, the permittivity recon-struction captures both zone and zone distributions. Theconductivity reconstruction is again able to reconstruct the (less)conductive zone (displacement dominated) satisfactorily. Inthe case of either displacement- or diffusion-dominated cases,an independent reconstruction of permittivity and conductivitycan be implemented. Fig. 8 shows a further example, wheresmall conductivity is present in both zone and zone , andboth permittivity and conductivity reconstructions perform sat-isfactorily. The skin depth in all the above cases is much largerthan the size of the imaging domain, and the permittivity dis-tribution is reconstructed without significant influence from theconductivity distribution.

432 IEEE SENSORS JOURNAL, VOL. 7, NO. 3, MARCH 2007

Fig. 10. Normalized reconstruction results for a two-sphere case, with the original distribution values depicted on the left.

Fig. 11. Normalized reconstruction of simulated data for a two-sphere case with the original distribution depicted on the left of the figure.

However, as mentioned above, reconstruction for a diffusiondominated regime may fail for large conductivity values corre-sponding to a skin depth below vessel size. This is illustrated inFig. 9, where the effect of a skin depth of (in the

S/m region) for a 1-m radius vessel is considered, andthe results obtained are not representative of the actual electricalproperty distribution.

Further examples are illustrated in Figs. 10 and 11, where twoseparate zones with different electrical properties coexist. In theexample of Fig. 10, both permittivity and conductivity distribu-tion are captured, but the permittivity distribution of the highconductivity region is affected by the reduced skin depth there(note the assymetry in the permittivity reconstruction). In theexample in Fig. 11, permittivity and conductivity distributionsare captured without significant skin effects.

VI. CONCLUSION

In this work, a noninvasive multimodal electrical tomographysystem based on ECT sensor hardware has been proposed. Thenew system is based on quasi-static analysis of ECT sensorsusing capacitance and power measurements for permittivity andconductivity imaging, respectively. A dual sensitivity matrix isobtained and integrated in an ILBP reconstruction algorithm.

The proposed tomography system overcomes the need forsensor contact and invasion when impedance imaging is per-formed based on current injection. Reconstruction results haveshowed the capability of the system in providing approximateconductivity and permittivity maps. The main limitations of thesystem are due to the neglect of nonlinearities, and to the skindepth effect at large conductivities.

Direct use of traditional reconstruction techniques, such asILBP, assumes independence between power and capacitancesignals. This is valid when one electrical property dominatesover the other in determining the measurement data. On theother hand, any correlation can be explored towards developingnew reconstruction techniques tailored for this problem in thefuture.

REFERENCES

[1] D. M. Scott and H. McCann, Process Imaging For Automatic Con-trol. New York: Taylor & Francis, 2005.

[2] R. A. Williams and M. S. Beck, Process Tomography: Principles,Techniques, and Applications. Oxford, U.K.: Butterworth-Heine-mann, 1995.

[3] M. S. Beck and R. A. Williams, “Process tomography: A European in-novation and its applications,” Meas. Sci. Technol., vol. 7, pp. 215–224,1996.

MARASHDEH et al.: MULTIMODAL TOMOGRAPHY SYSTEM 433

[4] W. Warsito and L.-S. Fan, “Neural network based multi-criterion op-timization image reconstruction technique for imaging two- and three-phase flow systems using electrical capacitance tomography,” Meas.Sci. Technol., vol. 12, pp. 2198–2210, 2001.

[5] B. T. Hjertaker, S.-A. Tjugum, E. A. Hammer, and G. A. Johansen,“Multimodality tomography for multiphase hydrocarbon flow mea-surements,” IEEE Sensors J., vol. 5, no. 2, pp. 153–160, Apr., 2005.

[6] T. York, “Status of electrical tomography in industrial applications,” J.Electron. Imag., vol. 10, no. 3, pp. 608–619, 2001.

[7] M. Cheney, D. Isakson, and J. C. Newell, “Electrical impedance to-mography,” SIAM Rev., vol. 41, no. 1, pp. 85–101, 1999.

[8] F. Dickin and M. Wang, “Electrical resistance tomography for processapplication,” Meas. Sci. Technol., vol. 7, pp. 247–260, 1996.

[9] E. D. Torre, The Electromagnetic Field. Boston, MA: Allyn andBacon, 1969.

[10] W. Q. Yang, “Hardware design of electrical capacitance tomographysystems,” Meas. Sci. Technol., vol. 7, pp. 225–232, 1996.

[11] R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Trans-mission and Radiation. New York: Wiley, 1960.

[12] W. Q. Yang and L. Peng, “Image reconstruction algorithms forelectrical capacitance tomography,” Meas. Sci. Technol., vol. 12, pp.R1–R13, 2003.

[13] O. Isakson, “A review of reconstruction techniques for capacitance to-mography,” Meas. Sci. Technol., vol. 7, pp. 325–337, 1996.

[14] J. C. Munk, T. J. C. Faes, and R. M. Heethaar, “The boundary elementmethod in the forward and inverse problem of electrical impedancetomography,” IEEE Trans. Biomed. Eng., vol. 47, no. 6, pp. 792–800,Jun. 2000.

[15] S. M. Huang, A. Plaskowski, C. G. Xie, and M. S. Beck, “Tomographicimaging of two-component flow using capacitance sensors,” J. Phys. E:Sci. Instrum., vol. 22, pp. 173–177, 1989.

[16] L. H. Peng, H. Merkus, and B. Scarlet, “Using regularization methodsfor image reconstruction of electrical capacitance tomography,” Part.Syst. Charact., vol. 17, pp. 96–104, 2000.

[17] Q. Marashdeh and F. L. Teixeira, “Sensitivity matrix calculation for fast3-D electrical capacitance tomography (ECT) of flow systems,” IEEETrans. Magn., vol. 40, no. 2, pp. 1204–1207, Mar. 2004.

[18] H. Yan, L. J. Liu, H. Xu, and F. Q. Shao, “Image reconstruction inelectrical capacitance tomography using multiple linear regression andregularzation,” Meas. Sci. Technol., vol. 12, pp. 575–581, 2001.

[19] K. L. Ostrowski, S. P. Luke, and R. A. Williams, “Application of conju-gate harmonics to electrical process tomography,” Meas. Sci. Technol.,vol. 7, pp. 316–324, 1996.

[20] W. Fang, “A nonlinear image reconstruction algorithm for electricalcapacitance tomography,” Meas. Sci. Technol., vol. 15, pp. 2124–2132,2004.

[21] Q. Marashdeh, W. Warsito, L.-S. Fan, and F. L. Teixeira, “Nonlinearforward problem solution for electrical capacitance tomography usingfeed-forward neural network,” IEEE Sensors J., vol. 6, no. 2, pp.441–449, Apr. 2006.

[22] M. Bertero, T. A. Pogcio, and V. Torre, “Ill-posed problems in earlyvision,” Proc. IEEE, vol. 76, no. 8, pp. 869–889, Aug. 1988.

Qussai Marashdeh (S’02–M’06) received the B.S.degree in electrical engineering from the Universityof Jordan, Amman, Jordan, in 2001, and the M.S.and Ph.D. degrees in electrical engineering fromthe Electroscience Laboratory, The Ohio StateUniversity (OSU), Columbus, in 2003 and 2006,respectively.

He is currently a Postdoctoral Researcher withthe Department of Chemical and BiomolecularEngineering, OSU. His research interests includeelectrical tomography systems, electrostatics, opti-

mization, neural network applications, and medical imagining.

Warsito Warsito (M’02) received the B. E. and M.E.degrees in chemical engineering and the Ph.D. degreein electronic science and technology from ShizuokaUniversity, Japan, in 1992, 1994, and 1997, respec-tively.

He is currently a Postdoctoral Research Associatewith the Department of Chemical and BiomolecularEngineering, The Ohio State University, Columbus,where he works on the development of electricalcapacitance tomography. His research interests arein the fields of tomography, ultrasound technology,

image reconstruction techniques, multiphase flow imaging and dynamics, andneural networks.

Liang-Shih Fan received the B.S. degree in chemicalengineering from National Taiwan University, Taipei,Taiwan, R.O.C., in 1970, the M.S. and Ph.D. degreesin chemical engineering from West Virginia Univer-sity, Morgantown, in 1973 and 1975, and the M.S. de-gree in statistics from Kansas State University, Man-hattan, in 1978.

He is a Distinguished University Professor andthe C. John Easton Professor in Engineering inthe Department of Chemical and BiomolecularEngineering, The Ohio State University, Columbus.

He is a member of the National Academy of Engineering and an Academicianof the Academia Sinica, Taiwan. His research interests include fluidization,multiphase flow, particulates reaction engineering, electrical tomography, andenergy and environmental engineering.

Fernando L. Teixeira (S’92–M’99–SM’03) re-ceived the B.S. and M.S. degrees in electricalengineering from the Pontifical Catholic University,Rio de Janeiro (PUC-Rio), Brazil, in 1991 and1995, respectively, and the Ph.D. degree in elec-trical engineering from the University of Illinois atUrbana-Champaign, Urbana, in 1999.

From 1999 to 2000, he was a Postdoctoral Re-search Associate with the Research Laboratory ofElectronics, Massachusetts Institute of Technology(MIT), Cambridge. Since 2000, he has been an As-

sistant Professor at the ElectroScience Laboratory (ESL) and the Department ofElectrical Engineering, The Ohio State University (OSU), Columbus. He editedthe book Geometric Methods for Computational Electromagnetics (EMW,2001, Progress in Electromagnetics Research Series 32), and has (co-)authoredover 60 journal articles and book chapters and over 80 conference publications.His research interests include computational electromagnetics, remote sensing,and inverse problems.

Dr. Teixeira was awarded many prizes for his research, including the LumleyResearch Award from OSU in 2004, the National Science Foundation CAREERAward in 2004, and the triennial USNC/URSI Henry Booker Fellowship in2005. He is a member of Phi Kappa Phi, Sigma Xi, and a full member of URSICommission B.