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Electrical Impedance Tomography
 SIAM REVIEW
, 1999
"... This paper surveys some of the work our group has done in electrical impedance tomography. ..."
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Cited by 82 (1 self)
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This paper surveys some of the work our group has done in electrical impedance tomography.
High contrast impedance tomography
 INVERSE PROBLEMS
, 1996
"... We introduce an output leastsquares method for impedance tomography problems that have regions of high conductivity surrounded by regions of lower conductivity. The high conductivity is modeled on network approximation results from an asymptotic analysis and its recovery is based on this model. The ..."
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Cited by 44 (6 self)
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We introduce an output leastsquares method for impedance tomography problems that have regions of high conductivity surrounded by regions of lower conductivity. The high conductivity is modeled on network approximation results from an asymptotic analysis and its recovery is based on this model. The smoothly varying part of the conductivity is recovered by a linearization process as is usual. We present the results of several numerical experiments that illustrate
Multiscale scientific computation: Review 2001
 Multiscale and Multiresolution Methods
, 2001
"... ..."
Exponential instability in an inverse problem for the Schrödinger equation
 Inverse Problems 17:5 (2001), 1435–1444. MR 2002h:35339 Zbl 0985.35110
"... Abstract. We consider the problem of the determination of the potential from the Dirichlet to Neumann map of the Schrödinger operator.We show that this problem is severely ill posed.The results extend to the electrical impedance tomography.They show that the logarithmic stability results of Alessand ..."
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Cited by 37 (0 self)
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Abstract. We consider the problem of the determination of the potential from the Dirichlet to Neumann map of the Schrödinger operator.We show that this problem is severely ill posed.The results extend to the electrical impedance tomography.They show that the logarithmic stability results of Alessandrini are optimal. 1
Uniqueness in the Inverse Conductivity Problem for Nonsmooth Conductivities in Two Dimensions
, 1997
"... this paper) imply, via Sobolev embedding, that the conductivity is continuous. It is interesting to note that the only uniqueness results available for conductivities which are discontinuous are due to Kohn and Vogelius [9] who study conductivities which are piecewise analytic and V. Isakov [8] who ..."
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Cited by 34 (9 self)
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this paper) imply, via Sobolev embedding, that the conductivity is continuous. It is interesting to note that the only uniqueness results available for conductivities which are discontinuous are due to Kohn and Vogelius [9] who study conductivities which are piecewise analytic and V. Isakov [8] who considers a class of conductivities which are piecewise C
Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction.
, 1998
"... We derive an asymptotic formula for the electrostatic voltage potential in the presence of a finite number of diametrically small inhomogeneities with conductivity different from the background conductivity. We use this formula to establish continuous dependence estimates and to design an effective ..."
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Cited by 23 (5 self)
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We derive an asymptotic formula for the electrostatic voltage potential in the presence of a finite number of diametrically small inhomogeneities with conductivity different from the background conductivity. We use this formula to establish continuous dependence estimates and to design an effective computational identification procedure. 1. Introduction 2. The electrostatic problem 3. An energy estimate 4. Some additional preliminary estimates 5. An asymptotic formula for the voltage potential 6. Properties of the polarization tensor 7. The continuous dependence of the inhomogeneities 8. Computational results. 9. References 1 Introduction The nondestructive inspection technique known as electrical impedance imaging has recently received considerable attention in the mathematical as well as in the engineering literature [2, 4, 10, 14, 17]. Using this technique one seeks to determine information about the internal conductivity (or impedance) profile of an object based on boundary i...
Numerical Method for Solving 3D Inverse Scattering Problems
, 1988
"... Let q(z) E L’(D), D C R3 is a bounded domain, q = 0 outside D, (I is realvalued. Assume that A(P, 0, k): = A(O’, 8), the scattering amplitude, is known for all B’, 0 E 9, Sz is the unit sphere, and a fixed I;> 0. These data determine q(z) uniquely and a numerical method is given for computing q(c ..."
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Cited by 18 (15 self)
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Let q(z) E L’(D), D C R3 is a bounded domain, q = 0 outside D, (I is realvalued. Assume that A(P, 0, k): = A(O’, 8), the scattering amplitude, is known for all B’, 0 E 9, Sz is the unit sphere, and a fixed I;> 0. These data determine q(z) uniquely and a numerical method is given for computing q(c).
Electric Field Imaging
, 1999
"... The physical user interface is an increasingly significant factor limiting the effectiveness of our interactions with and through technology. This thesis introduces Electric Field Imaging, a new physical channel and inference framework for machine perception of human action. Though electric field se ..."
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Cited by 18 (5 self)
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The physical user interface is an increasingly significant factor limiting the effectiveness of our interactions with and through technology. This thesis introduces Electric Field Imaging, a new physical channel and inference framework for machine perception of human action. Though electric field sensing is an important sensory modality for several species of fish, it has not been seriously explored as a channel for machine perception. Technological applications of field sensing, from the Theremin to the capacitive elevator button, have been limited to simple proximity detection tasks. This thesis presents a solution to the inverse problem of inferring geometrical information about the configuration and motion of the human body from electric field measurements. It also presents simple, inexpensive hardware and signal processing techniques for making the field measurements, and several new applications of electric field sensing. The signal