Resistor networks and optimal grids for the numerical solution of electrical impedance tomography with partial boundary measurements

This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/62096

[1]  David Isaacson,et al.  Layer stripping: a direct numerical method for impedance imaging , 1991 .

[2]  David Isaacson,et al.  NOSER: An algorithm for solving the inverse conductivity problem , 1990, Int. J. Imaging Syst. Technol..

[3]  Vladimir Druskin,et al.  Application of the Difference Gaussian Rules to Solution of Hyperbolic Problems , 2000 .

[4]  E. Somersalo,et al.  Existence and uniqueness for electrode models for electric current computed tomography , 1992 .

[5]  A. Calderón,et al.  On an inverse boundary value problem , 2006 .

[6]  R. Kohn,et al.  Relaxation of a variational method for impedance computed tomography , 1987 .

[7]  Giovanni Alessandrini,et al.  Stable determination of conductivity by boundary measurements , 1988 .

[8]  Giovanni Alessandrini,et al.  Singular solutions of elliptic equations and the determination of conductivity by boundary measurements , 1990 .

[9]  E. Reich Quasiconformal mappings of the disk with given boundary values , 1976 .

[10]  W. F. Tinney,et al.  On computing certain elements of the inverse of a sparse matrix , 1975, Commun. ACM.

[11]  D. Dobson,et al.  An image-enhancement technique for electrical impedance tomography , 1994 .

[12]  Juan Antonio Barceló,et al.  Stability of the Inverse Conductivity Problem in the Plane for Less Regular Conductivities , 2001 .

[13]  Robert V. Kohn,et al.  Determining conductivity by boundary measurements , 1984 .

[14]  A. Nachman,et al.  Reconstructions from boundary measurements , 1988 .

[15]  MATTI LASSAS,et al.  Calderóns' Inverse Problem for Anisotropic Conductivity in the Plane , 2004 .

[16]  Jenn-Nan Wang,et al.  Stability estimates for the inverse boundary value problem by partial Cauchy data , 2006 .

[17]  Alberto Ruiz,et al.  Stability of Calderón inverse conductivity problem in the plane , 2007 .

[18]  Liliana Borcea,et al.  INVERSE PROBLEMS PII: S0266-5611(02)33630-X Optimal finite difference grids for direct and inverse Sturm–Liouville problems , 2002 .

[19]  David C. Dobson,et al.  Convergence of a reconstruction method for the inverse conductivity problem , 1992 .

[20]  J C Newell,et al.  Reconstruction of conductivity changes due to ventilation and perfusion from EIT data collected on a rectangular electrode array. , 2001, Physiological measurement.

[21]  Robert V. Kohn,et al.  Numerical implementation of a variational method for electrical impedance tomography , 1990 .

[22]  E. Curtis,et al.  Inverse Problems for Electrical Networks , 2000 .

[23]  G. Uhlmann,et al.  The Calderón problem with partial data , 2004, math/0405486.

[24]  Kari Astala,et al.  Calderon's inverse conductivity problem in the plane , 2006 .

[25]  Murthy N. Guddati,et al.  On Optimal Finite-Difference Approximation of PML , 2003, SIAM J. Numer. Anal..

[26]  J. Berryman Weighted least-squares criteria for seismic traveltime tomography , 1989 .

[27]  F. G. Vasquez On the parameterization of ill-posed inverse problems arising from elliptic partial differential equations , 2006 .

[28]  A. Nachman,et al.  Global uniqueness for a two-dimensional inverse boundary value problem , 1996 .

[29]  Liliana Borcea,et al.  On the continuum limit of a discrete inverse spectral problem on optimal finite difference grids , 2005 .

[30]  David V. Ingerman,et al.  Discrete and Continuous Dirichlet-to-Neumann Maps in the Layered Case , 2000, SIAM J. Math. Anal..

[31]  David Isaacson,et al.  A direct reconstruction algorithm for electrical impedance tomography , 2002, IEEE Transactions on Medical Imaging.

[32]  R. Kohn,et al.  Determining conductivity by boundary measurements II. Interior results , 1985 .

[33]  David V. Ingerman,et al.  On a characterization of the kernel of the Dirichlet-to-Neumann map for a planar region , 1998 .

[34]  Liliana Borcea A nonlinear multigrid for imaging electrical conductivity and permittivity at low frequency , 2001 .

[35]  K. Strebel Extremal quasiconformal polygon mappings for arbitrary subdomains of compact Riemann surfaces , 2002 .

[36]  Liliana Borcea,et al.  Pyramidal resistor networks for electrical impedance tomography with partial boundary measurements , 2010 .

[37]  Y. C. Verdière,et al.  Reseaux électriques planaires II , 1994 .

[38]  Sun Wei-ling,et al.  Progress on Electrical Impedance Tomography , 2007 .

[39]  D. Isaacson,et al.  An implementation of the reconstruction algorithm of A Nachman for the 2D inverse conductivity problem , 2000 .

[40]  B. M. Levitan,et al.  Inverse Sturm-Liouville Problems , 1987 .

[41]  G. Uhlmann,et al.  RECOVERING A POTENTIAL FROM PARTIAL CAUCHY DATA , 2002 .

[42]  Michael Vogelius,et al.  A backprojection algorithm for electrical impedance imaging , 1990 .

[43]  I. Duff,et al.  Direct Methods for Sparse Matrices , 1987 .

[44]  Gunther Uhlmann,et al.  Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions , 1997 .

[45]  G. Golub,et al.  Structured inverse eigenvalue problems , 2002, Acta Numerica.

[46]  David Isaacson,et al.  Exact solutions to a linearized inverse boundary value problem , 1990 .

[47]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[48]  Niculae Mandache,et al.  Exponential instability in an inverse problem for the Schrodinger equation , 2001 .

[49]  D. Isaacson,et al.  A reconstruction algorithm for electrical impedance tomography data collected on rectangular electrode arrays , 1999, IEEE Transactions on Biomedical Engineering.

[50]  Robert M. Gray,et al.  Toeplitz and Circulant Matrices: A Review , 2005, Found. Trends Commun. Inf. Theory.

[51]  A. N. Tikhonov,et al.  REGULARIZATION OF INCORRECTLY POSED PROBLEMS , 1963 .

[52]  พงศ์ศักดิ์ บินสมประสงค์,et al.  FORMATION OF A SPARSE BUS IMPEDANCE MATRIX AND ITS APPLICATION TO SHORT CIRCUIT STUDY , 1980 .

[53]  Liliana Borcea,et al.  Electrical impedance tomography with resistor networks , 2008 .

[54]  David Isaacson,et al.  Effects of measurement precision and finite numbers of electrodes on linear impedance imaging algorithms , 1991 .

[55]  John Sylvester,et al.  An anisotropic inverse boundary value problem , 1990 .

[56]  J. Sylvester,et al.  A global uniqueness theorem for an inverse boundary value problem , 1987 .

[57]  James A. Morrow,et al.  Circular planar graphs and resistor networks , 1998 .

[58]  G. Papanicolaou,et al.  High-contrast impedance tomography , 1996 .

[59]  James A. Morrow,et al.  Finding the conductors in circular networks from boundary measurements , 1994 .