Combining spatial support information and shape-based method for tomographic imaging inside a microwave cylindrical scanner

References

• Bucci, OM, Crocco, L, and Isernia, T, 1999. Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups, J. Opt. Soc. Am. A 16 (1999), pp. 1788–1798.
   Google Scholar
• Bucci, OM, and Isernia, T, 1997. Electromagnetic inverse scattering: Retrievable information and measurement strategies, Radio Sci. 32 (1997), pp. 2123–2138.
   Web of Science ®Google Scholar
• Isernia, T, Pascazio, V, and Pierri, R, 1997. A nonlinear estimation method in tomographic imaging, IEEE Trans. Geosci. Remote Sens. 35 (1997), pp. 910–923.
   Web of Science ®Google Scholar
• Burger, M, and Osher, SJ, 2005. A survey on level set methods for inverse problems and optimal design, Eur. J. Appl. Math. 16 (2005), pp. 263–301.
   Web of Science ®Google Scholar
• Dorn, O, and Lesselier, D, 2006. Level set methods for inverse scattering, Inverse Probl. 22 (2006), pp. R67–R131.
   Web of Science ®Google Scholar
• Litman, A, Lesselier, D, and Santosa, F, 1998. Reconstruction of a two-dimensional binary obstacles by controlled evolution of a level-set, Inverse Probl. 14 (1998), pp. 685–706.
   Web of Science ®Google Scholar
• Santosa, F, 1996. A level-set approach for inverse problems involving obstacles, ESAIM: Control, Optim. Calculus Variations 1 (1996), pp. 17–33.
   Google Scholar
• Miller, EL, Kilmer, M, and Rappaport, C, 2000. A new shape-based method for object localization and characterization from scattered field data, IEEE Trans. Geosci. Remote Sensing 38 (2000), pp. 1682–1696.
   Web of Science ®Google Scholar
• Naik, N, Eriksson, J, de Groen, P, and Sahli, H, 2008. A nonlinear iterative reconstruction and analysis approach to shape-based approximate electromagnetic tomography, IEEE Trans. Geosci. Remote Sensing 46 (2008), pp. 1558–1574.
   Web of Science ®Google Scholar
• Zachoropoulos, A, Arridge, S, Dorn, O, Kolehmainen, V, and Sikora, J, 2006. Three-dimensional reconstruction of shape and piecewise constant region values for optical tomography using spherical harmonic parameterization and a boundary element method, Inverse Probl. 22 (2006), pp. 1509–1532.
   Web of Science ®Google Scholar
• Berre, I, Lien, M, and Mannseth, T, 2007. A level-set corrector to an adaptative multiscale permeability prediction, Comput. Geosci. 11 (2007), pp. 27–42.
   Web of Science ®Google Scholar
• Gelas, A, Bernard, O, Friboulet, D, and Prost, R, 2007. Compactly supported radial basis functions based collocation method for level-set evolution in image segmentation, IEEE Trans. Image Process. 16 (2007), pp. 1873–1887.
   PubMed Web of Science ®Google Scholar
• Bernard, O, Friboulet, D, Thevenaz, P, and Unser, M, 2008. Variational B-spline level-set method for fast image segmentation, IEEE Int. Symp. Biomed. Imaging (2008), pp. 177–180.
   Google Scholar
• Osher, S, and Sethian, JA, 1988. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations, J. Comput. Phys. 79 (1988), pp. 12–49.
   Web of Science ®Google Scholar
• Vese, L, and Chan, T, 2002. A multiphase level-set framework for image segmentation using the Mumford and Shah model, Int. J. Comp. Vision 50 (2002), pp. 271–293.
   Web of Science ®Google Scholar
• Lencrerot, R, Litman, A, Tortel, H, and Geffrin, JM, 2007. A microwave imaging circular setup for soil moisture information, IEEE Int. Symp. Geosci. Remote Sensing (2007), pp. 4394–4397.
   Google Scholar
• Jin, J, 2002. The Finite Element Method in Electromagnetics. New York: Willey-Interscience; 2002.
   Google Scholar
• Geuzaine, C, and Remacle, J-F, 2007. GMSH Reference Manual: A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities (2007), Available at http://www.geuz.org/gmsh.
   Google Scholar
• Demmel, JW, Eisenstat, SC, Gilbert, JR, Li, XS, and Liu, JWH, 1999. A supernodal approach to sparse partial pivoting, SIAM J. Matrix Anal. Appl. 20 (1999), pp. 720–755.
   Web of Science ®Google Scholar
• Nocedal, J, and Wright, SJ, 2006. Numerical Optimization. Berlin: Springer; 2006.
   Google Scholar
• Cmielewski, O, Tortel, H, Litman, A, and Saillard, M, 2007. A two-step procedure for characterizing obstacles under a rough surface, IEEE Trans. Geosci. Remote Sensing 45 (2007), pp. 185–200.
   Web of Science ®Google Scholar
• Abgrall, R, 1996. Numerical discretization of the first-order Hamilton–Jacobi equations on triangular meshes, Comm. Pure Apl. Math. 49 (1996), pp. 1339–1373.
   Google Scholar
• Born, M, and Wolf, E, 1959. Principles of Optics. Oxford: Pergamon Press; 1959.
   Google Scholar
• Crocco, L, and Litman, A, 2009. On embedded microwave imaging systems: Retrievable information and design guidelines, Inverse Probl. 25 (6) (2009), p. 065001.
   Web of Science ®Google Scholar
• Lencrerot, R, Litman, A, Tortel, H, and Geffrin, JM, 2009. Imposing Zernike representation for imaging two-dimensional targets, Inverse Probl. 25 (2009), p. 035012.
   Web of Science ®Google Scholar
• Chaudhari, A, Shankarwar, A, Arbad, B, and Mehrotra, S, 2004. Dielectric relaxation in glycine–water and glycine–ethanol–water solutions using time domain reflectometry, J. Sol. Chem. 33 (2004), pp. 313–322.
   Web of Science ®Google Scholar
• DeCezaro, A, Leitão, A, and Tai, XC, 2009. On multiple level-set regularization methods for inverse problems, Inverse Probl. 25 (2009), p. 035004.
   Web of Science ®Google Scholar
• Litman, A, 2005. Reconstruction by level-sets of n-ary scattering obstacles, Inverse Probl. 21 (2005), pp. S131–S152.
   Web of Science ®Google Scholar
• Dorn, O, and Villegas, R, 2008. History matching of petroleum reservoirs using a level set technique, Inverse Probl. 24 (2008), p. 035015.
   Web of Science ®Google Scholar
• Tanushev, NM, and Vese, LA, 2007. A piecewise-constant binary model for electrical impedance tomography, Inverse Probl. Imaging 1 (2007), pp. 423–435.
   Web of Science ®Google Scholar