Citation: |
[1] |
T. Arens, Why linear sampling works, Inverse Problems, 20 (2004), 163-173.doi: 10.1088/0266-5611/20/1/010. |
[2] |
T. Arens and A. Lechleiter, "The Linear Sampling Method Revisited," manuscript, 2007. |
[3] |
F. Cakoni and D. Colton, "Qualitative Methods in Inverse Scattering Theory: An Introduction," Interaction of Mechanics and Mathematics, Springer-Verlag, Berlin, 2006. |
[4] |
A. Charalambopoulos, D. Gintides and K. Kiriaki, The linear sampling method for the transmission problem in three-dimensional linear elasticity, Inverse Problems, 18 (2002), 547-558.doi: 10.1088/0266-5611/18/3/303. |
[5] |
D. Colton and A. Kirsch, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, 12 (1996), 383-393.doi: 10.1088/0266-5611/12/4/003. |
[6] |
D. Colton and R. Kress, "Inverse Acoustic and Electromagnetic Scattering Theory," 2nd Ed., Applied Mathematical Sciences, 93, Springer, Berlin, 1998. |
[7] |
D. Colton and P. Monk, A linear sampling method for the detection of leukemia using microwaves II, SIAM J. Appl. Math., 60 (1999), 241-255.doi: 10.1137/S003613999834426X. |
[8] |
D. Colton, M. Piani and R. Potthast, A simple method using Morozov's discrepancy principle for solving inverse scattering problems, Inverse Problems, 13 (1997), 1477-1493.doi: 10.1088/0266-5611/13/6/005. |
[9] |
H. W. Engl, M. Hanke and A. Neubauer, "Regularization of Inverse Problems," Mathematics and its Applications, 375, Kluwer Academic Publishers Group, Dordrecht, 1996. |
[10] |
B. Gebauer, M. Hanke, A. Kirsch, W. Muniz and C. Schneider, A sampling method for detecting buried objects using electromagnetic scattering, Inverse Problems, 21 (2005), 2035-2050.doi: 10.1088/0266-5611/21/6/015. |
[11] |
I. S. Gradshteyn and I. M. Ryzhik, "Table of Integrals, Series and Products," 7th Ed., Academic Press, New York, 2007. |
[12] |
C. W. Groetsch, "The Theory of Tikhonov Regularization for Fredholm Integral Equations of the First Kind," Research Notes in Mathematics, 105, Pitman (Advanced Publishing Program), Boston, MA, 1984. |
[13] |
H. Haddar and P. Monk, The linear sampling method for solving the electromagnetic inverse medium problem, Inverse Problems, 18 (2002), 891-906.doi: 10.1088/0266-5611/18/3/323. |
[14] |
A. Kirsch, Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems, 14 (1998), 1489-1512.doi: 10.1088/0266-5611/14/6/009. |
[15] |
A. Kirsch and N. Grinberg, "The Factorization Method for Inverse Problems," Oxford University Press, Oxford, 2008. |
[16] |
P. Monk, "Finite Element Methods for Maxwell's Equations," Numerical Mathematics and Scientific Computation. Oxford University Press, New York, 2003. |
[17] |
V. A. Morozov, On the solution of functional equations by the method of regularization, Dokl. Akad. Nauk SSSR, 167, 510-512 (Russian), translated as Soviet Math. Dokl., 7 (1966), 414-417. |
[18] |
V. A. Morozov, "Methods for Solving Incorrectly Posed Problems," Translated from the Russian by A. B. Aries. Translation edited by Z. Nashed. Springer-Verlag, New York, 1984. |
[19] |
S. Nintcheu Fata and B. B. Guzina, A linear sampling method for near-field inverse problems in elastodynamics, Inverse Problems, 20 (2004), 713-736.doi: 10.1088/0266-5611/20/3/005. |
[20] |
A. Tacchino, J. Coyle and M. Piana, Numerical validation of the linear sampling method, Inverse Problems, 18 (2002), 511-527.doi: 10.1088/0266-5611/18/3/301. |
[21] |
G. M. Vainikko, The discrepancy principle for a class of regularization methods, USSR Comp. Math. Math. Phys., 22 (1982), 1-19.doi: 10.1016/0041-5553(82)90120-3. |
[22] |
G. M. Vainikko, The critical level of discrepancy in regularization methods, USSR Comp. Math. Math. Phys., 23 (1983), 1-19.doi: 10.1016/S0041-5553(83)80068-8. |