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An improved fast local level set method for three-dimensional inverse gravimetry
1. | Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States, United States |
2. | Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong |
References:
[1] |
H. Bertete-Aguirre, E. Cherkaev and M. Oristaglio, Non-smooth gravity problem with total variation penalization functional, Geophys. J. Int., 149 (2002), 499-507.
doi: 10.1046/j.1365-246X.2002.01664.x. |
[2] |
M. Burger, A level set method for inverse problems, Inverse Problems, 17 (2001), 1327-1355.
doi: 10.1088/0266-5611/17/5/307. |
[3] |
M. Burger and S. Osher, A survey on level set methods for inverse problems and optimal design, European J. Appl. Math., 16 (2005), 263-301.
doi: 10.1017/S0956792505006182. |
[4] |
T. Cecil, S. J. Osher and J. Qian, Simplex free adaptive tree fast sweeping and evolution methods for solving level set equations in arbitrary dimension, J. Comput. Phys., 213 (2006), 458-473.
doi: 10.1016/j.jcp.2005.08.020. |
[5] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd edition, Springer, 2013.
doi: 10.1007/978-1-4614-4942-3. |
[6] |
T. DeLillo, V. Isakov, N. Valdivia and L. Wang, The detection of surface vibrations from interior acoustical pressure, Inverse Problems, 19 (2003), 507-524.
doi: 10.1088/0266-5611/19/3/302. |
[7] |
O. Dorn and D. Lesselier, Level set methods for inverse scattering, Inverse Problems, 22 (2006), R67-R131.
doi: 10.1088/0266-5611/22/4/R01. |
[8] |
S. Hou, K. Solna and H.-K. Zhao, Imaging of location and geometry for extended targets using the response matrix, J. Comput. Phys., 199 (2004), 317-338.
doi: 10.1016/j.jcp.2004.02.010. |
[9] |
V. Isakov, Inverse Source Problems, American Mathematical Society, Providence, Rhode Island, 1990.
doi: 10.1090/surv/034. |
[10] |
V. Isakov, S. Leung and J. Qian, A fast local level set method for inverse gravimetry, Comm. in Computational Physics, 10 (2011), 1044-1070.
doi: 10.4208/cicp.100710.021210a. |
[11] |
V. Isakov, S. Leung and J. Qian, A three-dimensional inverse gravimetry problem for ice with snow caps, {Inverse Problems and Imaging}, 7 (2013), 523-544.
doi: 10.3934/ipi.2013.7.523. |
[12] |
A. Litman, D. Lesselier and F. Santosa, Reconstruction of a 2-D binary obstacle by controlled evolution of a level-set, Inverse Problems, 14 (1998), 685-706.
doi: 10.1088/0266-5611/14/3/018. |
[13] |
W. Lu and Y. Y. Lu, Efficient boundary integral equation method for photonic crystal fibers, Journal of Lightwave Technology, 30 (2012), 1610-1616.
doi: 10.1109/JLT.2012.2189355. |
[14] |
S. J. Osher and J. A. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), 12-49.
doi: 10.1016/0021-9991(88)90002-2. |
[15] |
J. Qian, L.-T. Cheng and S. J. Osher, A level set based Eulerian approach for anisotropic wave propagations, Wave Motion, 37 (2003), 365-379.
doi: 10.1016/S0165-2125(02)00101-4. |
[16] |
J. Qian and S. Leung, A level set method for paraxial multivalued traveltimes, J. Comput. Phys., 197 (2004), 711-736.
doi: 10.1016/j.jcp.2003.12.017. |
[17] |
J. Qian and S. Leung, A local level set method for paraxial multivalued geometric optics, SIAM J. Sci. Comp., 28 (2006), 206-223.
doi: 10.1137/030601673. |
[18] |
F. Santosa, A level-set approach for inverse problems involving obstacles, Control, Optimizat. Calculus Variat., 1 (1996), 17-33. |
[19] |
K. van den Doel, U. Ascher and A. Leitao, Multiple level sets for piecewise constant surface reconstruction in highly ill-posed problems, J. Sci. Comput., 43 (2010), 44-66.
doi: 10.1007/s10915-009-9341-x. |
[20] |
H.-K. Zhao, T. Chan, B. Merriman and S. J. Osher, A variational level set approach for multiphase motion, J. Comput. Phys., 127 (1996), 179-195.
doi: 10.1006/jcph.1996.0167. |
show all references
References:
[1] |
H. Bertete-Aguirre, E. Cherkaev and M. Oristaglio, Non-smooth gravity problem with total variation penalization functional, Geophys. J. Int., 149 (2002), 499-507.
doi: 10.1046/j.1365-246X.2002.01664.x. |
[2] |
M. Burger, A level set method for inverse problems, Inverse Problems, 17 (2001), 1327-1355.
doi: 10.1088/0266-5611/17/5/307. |
[3] |
M. Burger and S. Osher, A survey on level set methods for inverse problems and optimal design, European J. Appl. Math., 16 (2005), 263-301.
doi: 10.1017/S0956792505006182. |
[4] |
T. Cecil, S. J. Osher and J. Qian, Simplex free adaptive tree fast sweeping and evolution methods for solving level set equations in arbitrary dimension, J. Comput. Phys., 213 (2006), 458-473.
doi: 10.1016/j.jcp.2005.08.020. |
[5] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd edition, Springer, 2013.
doi: 10.1007/978-1-4614-4942-3. |
[6] |
T. DeLillo, V. Isakov, N. Valdivia and L. Wang, The detection of surface vibrations from interior acoustical pressure, Inverse Problems, 19 (2003), 507-524.
doi: 10.1088/0266-5611/19/3/302. |
[7] |
O. Dorn and D. Lesselier, Level set methods for inverse scattering, Inverse Problems, 22 (2006), R67-R131.
doi: 10.1088/0266-5611/22/4/R01. |
[8] |
S. Hou, K. Solna and H.-K. Zhao, Imaging of location and geometry for extended targets using the response matrix, J. Comput. Phys., 199 (2004), 317-338.
doi: 10.1016/j.jcp.2004.02.010. |
[9] |
V. Isakov, Inverse Source Problems, American Mathematical Society, Providence, Rhode Island, 1990.
doi: 10.1090/surv/034. |
[10] |
V. Isakov, S. Leung and J. Qian, A fast local level set method for inverse gravimetry, Comm. in Computational Physics, 10 (2011), 1044-1070.
doi: 10.4208/cicp.100710.021210a. |
[11] |
V. Isakov, S. Leung and J. Qian, A three-dimensional inverse gravimetry problem for ice with snow caps, {Inverse Problems and Imaging}, 7 (2013), 523-544.
doi: 10.3934/ipi.2013.7.523. |
[12] |
A. Litman, D. Lesselier and F. Santosa, Reconstruction of a 2-D binary obstacle by controlled evolution of a level-set, Inverse Problems, 14 (1998), 685-706.
doi: 10.1088/0266-5611/14/3/018. |
[13] |
W. Lu and Y. Y. Lu, Efficient boundary integral equation method for photonic crystal fibers, Journal of Lightwave Technology, 30 (2012), 1610-1616.
doi: 10.1109/JLT.2012.2189355. |
[14] |
S. J. Osher and J. A. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), 12-49.
doi: 10.1016/0021-9991(88)90002-2. |
[15] |
J. Qian, L.-T. Cheng and S. J. Osher, A level set based Eulerian approach for anisotropic wave propagations, Wave Motion, 37 (2003), 365-379.
doi: 10.1016/S0165-2125(02)00101-4. |
[16] |
J. Qian and S. Leung, A level set method for paraxial multivalued traveltimes, J. Comput. Phys., 197 (2004), 711-736.
doi: 10.1016/j.jcp.2003.12.017. |
[17] |
J. Qian and S. Leung, A local level set method for paraxial multivalued geometric optics, SIAM J. Sci. Comp., 28 (2006), 206-223.
doi: 10.1137/030601673. |
[18] |
F. Santosa, A level-set approach for inverse problems involving obstacles, Control, Optimizat. Calculus Variat., 1 (1996), 17-33. |
[19] |
K. van den Doel, U. Ascher and A. Leitao, Multiple level sets for piecewise constant surface reconstruction in highly ill-posed problems, J. Sci. Comput., 43 (2010), 44-66.
doi: 10.1007/s10915-009-9341-x. |
[20] |
H.-K. Zhao, T. Chan, B. Merriman and S. J. Osher, A variational level set approach for multiphase motion, J. Comput. Phys., 127 (1996), 179-195.
doi: 10.1006/jcph.1996.0167. |
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