The crEITive software tool is based on and created together with the articles:
- F. Delbary, P. C. Hansen and K. Knudsen, Electrical impedance tomography: 3D reconstructions using scattering transforms, Applicable Analysis, 91 (2012), 737-755.
- F. Delbary and K. Knudsen, Numerical nonlinear complex geometrical optics algorithm for the 3D Calderon problem, Inverse Probl. Imaging, 8 (2014), 991-1012.
When using the software you may cite
@article{delbary2012a,
author = {Fabrice Delbary and Per Christian Hansen and Kim Knudsen},
title = {Electrical impedance tomography: 3{D} reconstructions using scattering transforms},
journal = {Applicable Analysis},
volume = {91},
number = {4},
pages = {737-755},
year = {2012},
publisher = {Taylor & Francis}
}
@article{delbary2014a,
AUTHOR = {Fabrice Delbary and Kim Knudsen},
title = {Numerical nonlinear complex geometrical optics algorithm for
the 3{D} {C}alder\'{o}n problem},
journal = {Inverse Probl. Imaging},
volume = {8},
year = {2014},
number = {4},
pages = {991--1012}
}
The three-dimensional Calderón problem and reconstruction algorithm is theoretically based on a number of seminal papers of the 1980s.
- A.-P. Calderon, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, Soc. Brasil. Mat., Rio de Janeiro, 1980, 65-73
- A. Nachman, J. Sylvester and G. Uhlmann, An n-dimensional Borg-Levinson theorem, Comm. Math. Phys., 115 (1988), 595-605
- A. Nachman, Reconstructions from boundary measurements, Ann. of Math. (2), 128 (1988), 531-576.
- R. Novikov, Multidimensional inverse spectral problem for the equation Δψ+ (v(x) – Eu(x))ψ = 0, Functional Analysis and Its Applications, 22 (1988), 263-272.
- J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. of Math. (2), 125 (1987), 153-169.