Novel Iterative Image Reconstruction Algorithm for ... - Semantic Scholar

IEICE TRANS. FUNDAMENTALS, VOL.E89–A, NO.6 JUNE 2006

1578

PAPER

Special Section on Papers Selected from ITC-CSCC 2005

Novel Iterative Image Reconstruction Algorithm for Electrical Capacitance Tomography: Directional Algebraic Reconstruction Technique∗ Ji Hoon KIM† , Bong Yeol CHOI† , Nonmembers, and Kyung Youn KIM††a) , Member

SUMMARY Electrical capacitance tomography (ECT) is used to obtain information about the distribution of a mixture of dielectric materials inside a vessel or pipe. ECT has several advantages over other reconstruction algorithms and has found many applications in the industrial fields. However, there are some difficulties with image reconstruction in ECT: The relationship between the permittivity distribution and measured capacitance is nonlinear. And inverse problem is ill-posed so that the inverse solution is sensitive to measurement error. To cope with these difficulties iterative image reconstruction algorithms have been developed. In general, the iterative reconstruction algorithms in ECT have comparatively goodquality in reconstructed images but result in intensive computational burden. This paper presents the iterative image reconstruction algorithm for ECT that can enhance the speed of image reconstruction without degradation in the quality of reconstructed image. The main contribution of the proposed algorithm is new weighting matrices, which are obtained by the interpolation of the grouped electrical field centre lines (EFCLs). Extensive simulation results have demonstrated that proposed algorithm provides improved reconstruction performance in terms of computational time and image quality. key words: electrical capacitance tomography, algebraic reconstruction technique, iterative image reconstruction algorithm

1.

Introduction

Electrical capacitance tomography (ECT) is used to obtain cross-sectional image about the distribution of a mixture of dielectric materials inside the process of interest, by measuring the capacitances between electrodes mounted its periphery and converting them into an image showing the distribution of permittivity. ECT has several advantages over other tomographic techniques; low-cost, rapid response, portability, no radiation hazard, but it has disadvantage of low-quality image. In the industrial area, ECT has found many applications; measurement of gas/liquid and gas/solids flows in pipelines, analysis of dynamic processes in fluidized beds, and visualization of combustion flames in engine cylinders [1]–[4]. Tomography sensor in general can be divided naturally Manuscript received September 8, 2005. Manuscript revised December 7, 2005. Final manuscript received February 14, 2006. † The authors are with the Department of Electrical Engineering, Kyungpook National University, Daegu, 702-701, Korea. †† The author is with the Department of Electrical & Electronic Engineering, Cheju National University, Jeju, 690-756, Korea. ∗ This paper was presented at the ITC-CSCC 2005 Oral Session THB3. a) E-mail: [email protected] DOI: 10.1093/ietfec/e89–a.6.1578

into two groups: ‘hard-field’ and ‘soft-field’ sensors. A ‘hard-field’ sensor is equally sensitive to the parameter it measures in all positions throughout the measurement volume. Its sensitivity is also independent of the distribution of the measured parameters inside and outside this measurement region. One of the examples of ‘hard-field’ sensor is medical tomography such as x-ray computerized tomography (CT). For a ‘soft-field’ sensor, on the other hand, sensitivity to the measured parameter depends on the position in the measurement volume, as well as on the distribution of parameters inside and outside this region. ECT is one of the examples of ‘soft-field’ sensor. There are two major computational procedures in ECT: the forward problem and inverse problem. The forward problem is to determine capacitance between electrodes from the known permittivity distribution by solving the governing equations (Poisson equation with Dirichlet boundary conditions). The inverse problem is to estimate the permittivity distribution from measured capacitances to present a cross-sectional image; hence this process is called image reconstruction. However, there are some difficulties in image reconstruction in ECT: 1) the relationship between the permittivity distribution and measured capacitance is highly nonlinear. Therefore it is almost impossible to establish an explicit expression, which relates the permittivity distribution to the measured capacitance. 2) Inverse problem is illposed so that the solution is sensitive to measurement error. 3) Inverse problem is also underdetermined since the number of unknowns is usually much larger than that of equations (the number of measured capacitances). Therefore, the solution is not unique. To overcome these difficulties, a number of algorithms have been developed. Currently, linear back-projection (LBP) algorithms are commonly used in ECT. They are simple and fast, but can only produce low-quality images. Also regularization methods are needed to treat the ill-posedness. Iterative image reconstruction algorithms were developed to address the nonlinearity and ill-posedness. In general, iterative algorithms produce improved images but they can only be used off-line because of their intensive computational burden [5], [6]. Therefore, one of the main concerns of ECT is to enhance the speed of image reconstruction in iterative image reconstruction algorithms. In this paper, we propose a novel iterative image reconstruction algorithm called directional algebraic reconstruc-

c 2006 The Institute of Electronics, Information and Communication Engineers Copyright

KIM et al.: NOVEL ITERATIVE IMAGE RECONSTRUCTION ALGORITHM FOR ELECTRICAL CAPACITANCE TOMOGRAPHY

1579

tion technique (DART). In the DART, new weighting matrices are obtained based on the interpolation of the grouped electrical field centre lines (EFCLs). The EFCL is formulated based on the assumption that the permittivity distribution inside the domain is homogeneous. To illustrate the performance of the proposed algorithm, extensive computer simulations are carried out for various scenarios and results show satisfactory performance in terms of image quality and computational time compared with the conventional algebraic reconstruction technique (ART) algorithm.

where Γ is the electrode surface. Using the charge Q at each detector electrode, the electrical capacitance C can be calculated as Q 1 C= =− ε(x, y)∇φ(x, y)dΓ (4) V V Γ

2.

2.2 Iterative Algorithms for Image Reconstruction

Electrical Capacitance Tomography

2.1 The Capacitance Measurement and Forward Solver The image reconstruction in ECT is to determine the permittivity distribution from measured capacitances. An ECT system can generally be divided into two parts; an ECT sensor for the measurement of capacitances between electrodes and a computer system for the image reconstruction using reconstruction algorithms. An ECT sensor consists of a number of electrodes placed around the process of interest. The measured capacitances between the electrodes are dependent on the dielectric constant of the medium in process. The capacitance measurements in ECT are obtained by a multiplexing unit and a number of capacitance detectors. For a 16-electrode sensor, electrodes 1–15 are used as source electrodes, one at the time. Electrode 1 is first excited at a voltage signal and the capacitance detectors 2–16, i.e. the detector electrodes, are used respectively to measure the capacitances between electrode 1 and the other electrodes. Next electrodes 2–15 are excited in sequence, so that capacitances of all electrodes pairs are measured. There are generally N = L(L − 1)/2 independent measurements for an L-electrode sensor, and hence a total number of independent measurements are 120 for a 16-electrode sensor. The measured capacitances are used to reconstruct the dielectric constant distribution based on the reconstruction algorithm. Theoretically the capacitance between electrodes can be obtained from the Poisson equation, which is given by ∇ · [ε(x, y)∇φ(x, y)] = −ρ(x, y)

(1)

where ε(x, y) is the permittivity distribution in sensing field, φ(x, y) is the potential distribution, and ρ(x, y) is the charge distribution, which is the source of the electrical field. Since there are no sources, i.e. no charges inside the sensor, Eq. (1) can be rewritten as ∇2 φ(x, y) +

1 ∇ε(x, y)∇φ(x, y) = 0 ε(x, y)

(2)

where the electrical field E(x, y) = −∇φ(x, y). In general, it is impossible to solve Eq. (2) for inhomogeneous permittivity distribution. Potential φ(x, y) can be calculated numerically by applying the finite element method (FEM). If the potential φ(x, y) is known, the charge Q of an electrode can be calculated using Gauss’s law

Q=−

ε(x, y)∇φ(x, y)dΓ Γ

(3)

where V is the potential difference between the source and detector electrode.

Image reconstruction algorithms in ECT can generally be classified into two groups; non-iterative algorithms and iterative algorithms. Since the relationship between the permittivity distribution and measured capacitance is nonlinear, it is almost impossible to find an accurate solution by any single-step, i.e. non-iterative algorithm with a simplified linear model. To improve the image quality, the inverse problem has to be solved iteratively. Iterative reconstruction algorithms in ECT are based on calculating capacitances from the permittivity distribution of the current iteration, and then producing a new image using the difference between the measured capacitance and calculated capacitance. This process is repeated until a satisfactory error bound is achieved or a fixed number of iterations are reached. Although there exist many different iterative algorithms, their basic principles are similar [5]. In the following, we only consider iterative algorithms; LBP with Landweber and ART [7], [8]. 2.2.1 LBP with Landweber As already stated above, the relationship between the permittivity distribution and measured capacitance is nonlinear. However, if the difference between the dielectric constants of constituent materials is small, a simple linear approximation can be made as follows: C∗ = S g

(5)

∗

where C is the normalized capacitance vector, S is the sensitivity matrix of normalized capacitance with respect to normalized permittivity, and g is the normalized permittivity vector. The normalized capacitance C ∗ is defined as follows: C∗ =

C − CL CH − CL

(6)

where C is measured capacitance, C L and C H are the capacitances when the sensor is filled with the materials of lower and higher permittivities, respectively. The LBP algorithm was the first algorithm used to reconstruct an image from capacitance data [9]. This algorithm is still the most commonly used image reconstruction algorithm in ECT. This algorithm is simple and fast but the image quality is not satisfied. LBP with Landweber was recently proposed for improving the image quality. This algorithm is defined as follows:


1580

g0 = S T C ∗ , gi+1 = gi − αS T (S gi − C ∗ )

(7) (8)

where α is the relaxation factor and T is transpose. In this algorithm the first image vector is reconstructed using LBP, i.e. using Eq. (7). (S gi −C ∗ ) is the error between a calculated capacitance vector S gi and the measured capacitance vector C ∗ . The error is used to reconstruct an error image S T (S gi − C ∗ ) and then used to correct the next image [7].

(a)

(b)

Fig. 1 Electrical field centre line: (a) The EFCL between electrodes 4 and 15; (b) adjacent regions to the EFCL between electrodes 4 and 15.

2.2.2 ART The ART is commonly used for image reconstruction in xray CT [10], [11]. They are simple and effective, especially when the system matrix is very large. ART has been applied to ECT [8]. This algorithm enhances the performance of the image reconstruction compared with the LBP algorithm, but suffers from noise in the measurement capacitance. The ART algorithm for ECT based on Eq. (5) is as follows: gi = gi−1 −

(si gi−1 − c∗i ) si sTi

· sTi

(9)

where si is the ith row vector of the sensitivity matrix and c∗i is the ith component of C ∗ . The ith update of the ART algorithm is based on the ith row in Eq. (5). In other words, the ith normalized capacitances in ith update only are used to update normalized permittivity distribution vector. If i = 1, 2, · · · , N, one iteration in ART is completed after N times update. 3.

Directional Algebraic Reconstruction Technique

Compared to the medical tomography such as x-ray CT, ECT differs in two respects: Firstly, the number of sensors placed around the process of interest is limited in process tomography. Secondly, since medical tomographs are generally based on ‘hard-field’ sensors, ‘hard-field’ sensor system sets up a uniform narrow field for which the sensitivity is independent of the parameter distribution inside the sensor. On the other hand, ECT is based on ‘soft-field’ sensors. This type of sensor generates an inhomogeneous field and the sensitivity distribution inside the field depends on the parameter distribution. Due to these characteristics the commonly used reconstruction algorithms developed for x-ray CT cannot be directly implemented into ECT [6]. Therefore, appropriate assumptions and approximations are needed to apply the reconstruction algorithms developed for x-ray CT to ECT. In this Sect., the development of the DART algorithm is outlined. 3.1 The Definition and Directional Grouping of EFCL The reconstruction algorithms developed for x-ray CT generally defines the ray-path running between the source and detector, which is a straight line with width. However, since an ECT sensor is ‘soft-field’ sensor, it is difficult to find an

accurate ray-path running between the source and detector. Although we can find the ray-path, it depends on the parameter distribution inside the sensor and then is changed according to the parameter distribution. To apply ART to ECT, we use the EFCL between the electrodes as the raypath, which is the fixed line by appropriate assumptions and approximation. The EFCL between electrodes is to approximate the line on the centre of the existing electrical field line based on the assumption that the sensor is circular and has homogeneous permittivity. Figure 1(a) shows the EFCL between electrodes 4 and 15 for the 16-electrode sensors (L = 16), and then the total number of EFCLs is N = 120, which is the same number as independent measurements. The ray-sum of the EFCL between specific electrodes is defined as the measured capacitance between corresponding electrodes. Figure 1(b) shows the adjacent regions which affect the EFCL between electrodes 4 and 15. It will be explained in Sect. 3.2 as a forward-weighting matrix. To consider the approximated EFCLs, we sort the groups with 7 or 8 EFCLs, which do not intersect each other as Fig. 2. Each group indicates a projection, which is called direction in this paper. In the direction, the number of EFCLs Nd is defined as 7, if 1, 3, · · · , 15th direction Nd = (10) 8, if 2, 4, · · · , 16th direction. Each group can classify into 8 directions and the total number of directions is 16, which is the same number as electrodes. 3.2 Weighting Matrices Based on Interpolation In x-ray CT, an image is reconstructed using the relationship between ray-path and elements passing by the ray-path (Fig. 3). In most cases in x-ray CT, the ray-path width is approximately equal to the image cell width and then parallel projections pass through all elements in the sensor [11]. But EFCLs in a direction do not pass through all elements in the sensor (Fig. 4). Therefore, to consider the relationship of EFCLs in a direction and the elements which are not passed by the EFCLs, we define the weighting matrices based on the distance between the centre of element and adjacent EFCLs. Two types of weighting matrices are needed to develop DART.


1581

The backward-weighting matrix WiB relates EFCLs in ith direction to all elements in the domain. g = WiBCi∗

(11) Ci∗

is the where g is the normalized permittivity vector and normalized capacitance vector in ith direction. The sensitivity distribution in the sensor, i.e. the weighting matrix, generally depends on the parameter distribution. However, the closer in the distance between a raypath and an element, the larger in sensitivity factor. Therefore we assume that the existing elements between adjacent EFCLs in a direction only influence the EFCLs. In Fig. 4, two bold lines are jth and j + 1th EFCLs in kth direction and triangles are elements to reconstruct the permittivity distribution in the domain and the point in a triangle is the centre of gravity of the triangle. The weighing factors between the EFCLs L j and L j+1 in kth direction and ith element are defined as d2 d1 WkB (i, j) = , W B (i, j + 1) = , (12) d1 + d2 k d1 + d2 i = 1, 2, · · · , M, j = 1, 2, · · · , Nd , k = 1, 2, · · · , L

Fig. 2

Six directions of EFCLs.

where M is the number of all elements in the domain, Nd is the number of EFCLs in a direction, and L is the number of electrode. In Eq. (12), d1 = 0 so that WkB (i, j) = 1 and WkB (i, j + 1) = 0 when ci is located on L j . In particular, we assume that the backward-weighting factor is equal to 1 when ci is located outside the EFCLs L1 and LNd . The forward-weighting matrix WiF relates all elements in the sensor to the EFCLs in ith direction and defined as WiF = [WiB ]T

(13)

where T denotes transpose. The sum of a row in forward- and backward-weighting matrices in kth direction is unity as follows: M

WkF (i, j) = 1,

j=1

Nd

WkB (i, j) = 1.

(14)

j=1

Since the used FEM mesh for reconstruction and EFCL between electrodes is fixed a priori, weighting matrices can be precalculated off-line so that online computational burden can be reduced significantly in image reconstruction. 3.3 DART Fig. 3

The concept of weighting matrix in x-ray CT.

In previous Sects., we developed weighting matrices based on the EFCLs to apply the reconstruction algorithms for xray CT to ECT. Using these weighting matrices, DART can be summarized as follows: gi+1 = gi + WiB (Ci∗ − WiF gi ), i = 1, 2, · · · , L

(15)

and WiF where gi is the normalized permittivity vector, are the backward- and forward-weighting matrices in ith direction, respectively defined in Sect. 3.2. Ci∗ is the normalized capacitance vector in ith direction. The ith update in the DART is based on the weighting matrices and normalized capacitances of the ith direction. Iteration in DART is completed after L times update, for the L-electrode sensor. WiB

Fig. 4

The concept of weighting matrix in ECT.


1582

4.

Computer Simulations and Results

In order to illustrate the reconstruction performance of the proposed weighting matrix-based ART algorithms, extensive computer simulations for diverse situations were carried out and compared with conventional sensitivity matrixbased ART algorithm. For image reconstruction, we used the domain with 1948 triangular elements (i.e. M = 1948) and 1039 nodes as shown in Fig. 5. The used domain has 80 mm in diameter and 16 electrodes (i.e. L = 16). For 16-electrode sensor, the number of independent measurements is N = 120. The low and high permittivity materials were air and water with permittivity values of 1 and 80, respectively. We simulated for three cases to confirm the reconstruction performance of proposed algorithm. Figure 6 shows three different permittivity distributions. Case 1 is that a waterdrop exists at the centre of domain containing air. Case 2 is that a waterdrop exists near the boundary of the domain and case 3 is that three waterdrops exist near the boundary. In all simulations the initial guess g0 is set to zero vector.

weighting matrices. Finally, the same weighting matrix used in the ART W is incorporated into the proposed DART. Reconstructed images for the three assumed scenarios are shown in Figs. 7–9. The images in the first, second, and third rows of Figs. 7–9 are reconstructed from ART S, ART W, and DART, respectively. The images in the first, second, and third columns of Figs. 7–9 represent reconstructed images at 1st, 5th, and 30th iteration steps, respectively. From these reconstructed images, it should be noted that the reconstruction performance of the proposed ART W and DART were enhanced than that of the conventional ART S. Note that the proposed ART W and DART can find approximate location and the size of the target(s) after first iteration. Among the proposed reconstruction algorithms, DART shows slightly improved reconstruction performance than ART W even

4.1 Evaluation of Reconstructed Images In this Sect., three reconstruction algorithms are employed to evaluate reconstruction performance. First of all, we used conventional ART algorithm with sensitivity matrix (ART S) in Eq. (9) as a reference algorithm. Secondly, the proposed weighting matrix described in Sect. 3.2 is incorporated into the conventional ART algorithm instead of the sensitivity matrix (ART W). In this case, the overall weighting matrix can be constructed by augmenting the backwardFig. 7 Reconstructed images for case 1 in Fig. 6 (the first, second, and third row images are obtained from ART S, ART W, and DART, respectively).

Fig. 5

Fig. 6

The used FEM mesh.

True permittivity distributions used in the simulations.

Fig. 8 Reconstructed images for case 2 in Fig. 6 (the first, second, and third row images are obtained from ART S, ART W, and DART, respectively).


1583

Fig. 9 Reconstructed images for case 3 in Fig. 6 (the first, second, and third row images are obtained from ART S, ART W, and DART, respectively).

though the same weighting matrices are used. 4.2 Evaluation of Errors In order to evaluate the reconstruction performance more quantitatively, image error (IE) and correlation coefficient (CC) were defined as follows: ˆg − g , g M ¯ˆ )(gi − g¯ ) i=1 (gî − g CC ≡ M M ¯ˆ )2 i=1 (gi − g¯ )2 i=1 (gî − g

IE ≡

(16)

Fig. 10 cases.

Table 1

(17)

where gˆ is the permittivity vector of reconstructed image, g is the permittivity vector of true image, and g¯ and g¯ˆ are the mean values of g and gˆ , respectively. The smaller IE and the closer CC to 1 give the better reconstruction performance. Figures 10(a), (c), and (e) show the IEs for cases 1, 2, and 3 in Fig. 6, respectively. As can be expected from the reconstructed images shown in Figs. 7–9, the IEs of the proposed ART W and DART are smaller than that of the conventional ART S for all assumed scenarios. In particular, DART has the smallest IE among the three reconstruction algorithms for all cases. Figures 10(b), (d), and (f) represent the CCs for cases 1, 2, and 3 in Fig. 6, respectively. As can be seen clearly in these figures, the CCs of the proposed ART W and DART are closer to 1 than that of the conventional ART S. Among the proposed reconstruction algorithms, ART W reveals slightly improved results during transient period in cases 2 and 3. However, DART would give the best CC if we take into account calculation time required for one iteration (see Sect. 4.3). 4.3 Evaluation of Computational Time In order to compare the reconstruction speed we consider

The comparison of image error and correlation coefficient for all

The calculation time per iteration [sec.].

Method Calculation Time

ART S 0.094

ART W 0.094

DART 0.031

the calculation time taken to obtain one image. The proposed algorithm was implemented using MatlabTM on a PC with a PentiumTM IV (2.4 GHz CPU and 512 Mbytes RAM). Table 1 shows the calculation time required for one iteration of each reconstruction algorithms. As can be seen in Table 1, the calculation time needed for one iteration of DART is just one-third of those of the ART S and ART W. It seems that the calculation time is reduced in DART since we used a predefined direction. Therefore, we can say that DART shows improved reconstruction performance with reduced computational burden. 5.

Conclusions

One of the main issues in electrical capacitance tomography is to reduce computational time in reconstruction algorithms without loss of image quality. In this paper, we proposed a novel iterative image reconstruction algorithm called DART. In the DART, new weighting matrices are obtained based on the interpolation of the grouped EFCLs. The EFCL is formulated based on the assumption that the permittivity distribution inside the domain is homogeneous.


1584

The advantages of the proposed algorithm are as follows: 1) the convergence rate of the weighting matrix based ART has better than that of sensitivity matrix based ART. 2) Weighting matrices can be precalculated off-line since FEM meshes and EFCL between electrodes is fixed a priori so that on-line reconstruction time can be reduced significantly. 3) DART can obtain comparatively good quality image in the initial stage so that it has strong potential for real-time reconstruction. Acknowledgments The authors would like to thank the anonymous reviewers for their helpful comments. References [1] M.S. Beck, A.B. Plaskowski, and R.B. Green, “Imaging for measurements of two-phase flow,” Proc. Flow Visualisation IV, Paris, pp.585–588, Hemisphere, London, Aug. 1986. [2] Ø. Isaksen, A.S. Dico, and E.A. Hammer, “A capacitance based tomography system for interface measurement in separation vessels,” Meas. Sci. Technol., vol.5, pp.1262–1271, 1994. [3] G.E. Fasching and N.S. Smith, “A capacitive system for 3dimensional imaging of fluidized beds,” Rev. Sci. Instrum., vol.62, pp.2243–2251, 1991. [4] R. He, C.G. Xie, R.C. Waterfall, M.S. Beck, and M.C. Beck, “Engine flame imaging using electrical capacitance tomography,” Electron. Lett., vol.30, pp.559–560, 1994. [5] W.Q. Yang and L. Peng, “Image reconstruction algorithms for electrical capacitance tomography,” Meas. Sci. Technol., vol.14, pp.R1– R13, 2003. [6] Ø. Isaksen, “A review of reconstruction techniques for capacitance tomography,” Meas. Sci. Technol., vol.7, pp.325–337, 1996. [7] W.Q. Yang, D.M. Spink, T.A. York, and H. McCann, “An image reconstruction algorithm based on Landweber’s iteration method for electrical capacitance tomography,” Meas. Sci. Technol., vol.10, pp.1065–1069, 1999. [8] N. Reinecke and D. Mewes, “Recent developments and industrial/research applications of capacitance tomography,” Meas. Sci. Technol., vol.7, pp.233–246, 1996. [9] C.G. Xie, S.M. Huang, B.S. Hoyle, R. Thorn, C. Lenn, and M.S. Beck, “Electrical capacitance tomography for flow imaging— System model for development of reconstruction algorithms and design of primary sensors,” IEE Proc.-G, vol.139, pp.89–98, 1992. [10] R. Gordon, R. Bender, and G.T. Herman, “Algebraic reconstruction techniques (ART) for three dimensional electron microscopy and Xray photography,” J. Theor. Biol., vol.29, pp.471–481, 1970. [11] A.C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, IEEE, New York, 1988.

Ji Hoon Kim received the B.S. degree in electrical control engineering from Kumoh National Institute of Technology, Gyeongbuk, Korea, in 2000 and the M.S. degree in electrical engineering in 2002 from Kyungbook National University, Daegu, Korea, where he is currently pursuing the Ph.D. degree. His research interests include the electrical impedance tomography, electrical capacitance tomography, and parameter estimation.

Bong Yeol Choi received the B.S. degrees in electronic engineering from Kyungbook National University, Daegu, Korea, in 1983, M.S. and Ph.D. degree from the Korea Advanced Institute of Science and Technology, Daejon, Korea, in 1985 and 1993, respectively. He is now Professor at The School of Electrical Engineering and Computer Science, Kyungpook National University, Daegu, Korea. His research area is electrical tomography and parameter estimation.

Kyung Youn Kim received the B.S., M.S., and Ph.D. degrees in electronic engineering from Kyungbook National University, Daegu, Korea, in 1983, 1986, and 1990, respectively. From 1994 to 1995, he was with the Department of Electrical Engineering, University of Maryland at Baltimore County (UMBC), MD, as a Postdoctoral Fellow. From 2001 to 2002, he was with the Department of Applied Physics, Kuopio University, Kuopio, Finland, as a Visiting Professor. From 2004 to 2005, he was with the Department of Biomedical Engineering, Rensselaer Polytechnic Institute (RPI), Troy, NY, as a Visiting Professor. Since 1990, he has been with Department of Electronic Engineering, Cheju National University, Jeju, Korea, where he is currently a Professor. His current research interests include estimation theory, inverse problems, intelligent fault detection and diagnosis, and electrical impedance tomography.