References
- Calderón , AP . 1980 . On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, Rio de Janeiro, 1980 , 65 – 73 . Rio de Janeiro : Sociedade Brasileira de Matemática .
- Holder (ed.) , DS . 2004 . Electrical Impedance Tomography: Methods, History And Applications , Bristol , , UK : Series in Medical Physics and Biomedical Engineering, Institute of Physics Publishing .
- Sylvester , J and Uhlmann , G . 1987 . A global uniqueness theorem for an inverse boundary value problem . Ann. of Math. (2) , 125 : 153 – 169 .
- Brown , RM and Torres , RH . 2003 . Uniqueness in the inverse conductivity problem for conductivities with 3/2 derivatives in L p , p > 2n . J. Fourier Anal. Appl. , 9 : 563 – 574 .
- Päivärinta , L , Panchenko , A and Uhlmann , G . 2003 . Complex geometrical optics solutions for Lipschitz conductivities . Rev. Mat. Iberoamericana , 19 : 57 – 72 .
- Novikov , RG . 1988 . A multidimensional inverse spectral problem for the equation −Δψ + (v(x) − Eu(x))ψ = 0 . Funktsional. Anal. Prilozhen. , 22 : 11 – 22 . 96
- Nachman , AI . 1988 . Reconstructions from boundary measurements . Ann. of Math. (2) , 128 : 531 – 576 .
- Nachman , AI . 1996 . Global uniqueness for a two-dimensional inverse boundary value problem . Ann. Math. , 143 ( 2 ) : 71 – 96 .
- Siltanen , S , Mueller , JL and Isaacson , D . 2000 . An implementation of the reconstruction algorithm of A. Nachman for the 2D inverse conductivity problem . Inverse Probl. , 16 : 681 – 699 .
- Siltanen , S , Mueller , J and Isaacson , D . 2001 . Erratum: An implementation of the reconstruction algorithm of A. Nachman for the 2D inverse conductivity problem [Inverse Probl. 16(3) (2000), pp. 681–699, MR1766226 (2001g:35269)] . Inverse Problems , 17 : 1561 – 1563 .
- Mueller , JL and Siltanen , S . 2003 . Direct reconstructions of conductivities from boundary measurements . SIAM J. Sci. Comput. , 24 : 1232 – 1266 .
- Knudsen , K , Lassas , M , Mueller , JL and Siltanen , S . 2007 . D-bar method for Electrical Impedance Tomography with discontinuous conductivities . SIAM J. Appl. Math. , 67 : 893 – 913 .
- Knudsen , K , Lassas , M , Mueller , JL and Siltanen , S . 2008 . Reconstructions of piecewise constant conductivities by the D-bar method for electrical impedance tomography . J. Phys. Conf. Ser. 2008 . Vol. 124 , pp. 012029
- Knudsen , K , Lassas , M , Mueller , JL and Siltanen , S . 2009 . Regularized D-bar method for the inverse conductivity problem . Inverse Probl. Imaging , 3 : 599 – 624 .
- Bikowski , J , Knudsen , K and Mueller , JL . 2011 . Direct numerical reconstruction of conductivities in three dimensions using scattering transforms . Inverse Probl. , 27 : 015002 (19 pp.)
- Knudsen , K and Mueller , JL . The Born approximation and Calderón's method for reconstruction of conductivities in 3-D, Discrete Contin. Dyn. Syst., Supplement 2011, pp. 884–893
- Astala , K and Päivärinta , L . 2006 . Calderón's inverse conductivity problem in the plane . Ann. Math. , 163 ( 2 ) : 265 – 299 .
- Astala , K , Mueller , JL , Päivärinta , L , Peramaki , A and Siltanen , S . Direct electrical impedance tomography for non-smooth conductivities, Inverse Probl. Imaging, 5 (2011), pp. 531–549
- Brühl , M . 2001 . Explicit characterization of inclusions in electrical impedance tomography . SIAM J. Math. Anal. , 32 : 1327 – 1341 . (electronic)
- Brühl , M and Hanke , M . 2000 . Numerical implementation of two noniterative methods for locating inclusions by impedance tomography . Inverse Probl. , 16 : 1029 – 1042 .
- Kirsch , A and Grinberg , N . 2008 . “ The Factorization Method for Inverse Problems ” . In Oxford Lecture Series in Mathematics and its Applications , Vol. 36 , Oxford : Oxford University Press .
- Eckel , H and Kress , R . 2007 . Nonlinear integral equations for the inverse electrical impedance problem . Inverse Probl. , 23 : 475 – 491 .
- Eckel , H and Kress , R . 2008 . Non-linear integral equations for the complete electrode model in inverse impedance tomography . Appl. Anal. , 87 : 1267 – 1288 .
- Borcea , L . 2002 . Electrical impedance tomography . Inverse Probl. , 18 : R99 – R136 .
- Cornean , H , Knudsen , K and Siltanen , S . 2006 . Towards a d-bar reconstruction method for three-dimensional EIT . J. Inverse Ill-Posed Probl. , 14 : 111 – 134 .
- Faddeev , LD . 1965 . Increasing solutions of the Schrödinger equation . Dokl. Akad. Nauk SSSR 165 , : 514 – 517 . (transl. Sov. Phys. Dokl. 10(1966), 1033–1035)
- DeAngelo , M and Mueller , JL . 2010 . 2D D-bar reconstructions of human chest and tank data using an improved approximation to the scattering transform . Physiol. Meas. , 31 : 221 – 232 .
- Mueller , JL and Siltanen , S . 2003 . Direct reconstructions of conductivities from boundary measurements . SIAM J. Sci. Comput. , 24 : 1232 – 1266 .
- Boverman , G , Kao , TJ , Isaacson , D and Saulnier , GJ . 2009 . An implementation of Calderón's Method for 3-D Limited-View EIT . IEEE Trans. Med. Imaging , 28 : 1073 – 1082 .
- Kress , R . 1999 . “ Linear Integral Equations ” . In Applied Mathematical Sciences, 2nd ed. , Vol. 82 , New York : Springer-Verlag .
- Colton , D and Kress , R . 1998 . “ Inverse acoustic and electromagnetic scattering theory ” . In Applied Mathematical Sciences, 2nd ed. , Vol. 93 , Berlin : Springer-Verlag .
- Boost C++ Libraries; http://www.boost.org
- Anderson , E , Bai , Z , Bischof , C , Blackford , S , Demmel , J , Dongarra , J , Du Croz , J , Greenbaum , A , Hammarling , S , McKenney , A and Sorensen , D . 1999 . “ LAPACK Users' Guide, 3rd ed. ” . In Society for Industrial and Applied Mathematics Philadelphia , PA
- The OpenMP® API specification for parallel programming; http://openmp.org
- Open MPI: Open source high performance computing; http://www.open-mpi.org
- Wienert , L . 1990 . Die numerische approximation von Randintegraloperatoren für die Helmholtzgleichung im ℝ3, Ph.D. Thesis , Georg-August-Universität Göttingen .
- Sloan , IH . 1995 . Polynomial interpolation and hyperinterpolation over general regions . J. Approx. Theory , 83 : 238 – 254 .
- Hesse , K and Sloan , IH . 2007 . “ Hyperinterpolation on the Sphere ” . In Frontiers in Interpolation and Approximation , 213 – 248 . Boca Raton , FL : Chapman & Hall/CRC .