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Microlocal aspects of common offset synthetic aperture radar imaging
1. | Department of Mathematics, Tufts University, 503, Boston Avenue, Medford, MA 02155, United States, United States |
References:
[1] |
L.-E. Andersson, On the determination of a function from spherical averages, SIAM J. Math. Anal., 19 (1988), 214-232.
doi: 10.1137/0519016. |
[2] |
M. Cheney, A mathematical tutorial on synthetic aperture radar, SIAM Rev., 43 (2001), 301-312.
doi: 10.1137/S0036144500368859. |
[3] |
M. Cheney and B. Borden, "Fundamentals of Radar Imaging," CBMS-NSF Regional Conference Series in Applied Mathematics, 79, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pennsylvania, 2009. |
[4] |
J. Duistermaat, "Fourier Integral Operators," Birkhäuser Boston, Inc., Boston, Massachusetts, 1996. |
[5] |
J. Cohen and H. Bleistein, Velocity inversion procedure for acoustic waves, Geophysics, 44 (1979), 1077-1085.
doi: 10.1190/1.1440996. |
[6] |
T. Dowling, "Radar Imaging Using Multiply Scattered Waves," Ph.D. Thesis, University of Limerick, Ireland, 2009. |
[7] |
R. Felea, Composition of Fourier integral operators with fold and blowdown singularities, Comm. Partial Differential Equations, 30 (2005), 1717-1740. |
[8] |
R. Felea, Displacement of artefacts in inverse scattering, Inverse Problems, 23 (2007), 1519-1531.
doi: 10.1088/0266-5611/23/4/009. |
[9] |
R. Felea and A. Greenleaf, An FIO calculus for marine seismic imaging: Folds and cross caps, Comm. P.D.E., 33 (2008), 45-77.
doi: 10.1080/03605300701318716. |
[10] |
A. Greenleaf and G. Uhlmann, Non-local inversion formulas for the X-ray transform, Duke Math. J., 58 (1989), 205-240.
doi: 10.1215/S0012-7094-89-05811-0. |
[11] |
A. Greenleaf and G. Uhlmann, Estimates for singular Radon transforms and pseudodifferential operators with singular symbols, J. Functional Anal., 89 (1990), 202-232.
doi: 10.1016/0022-1236(90)90011-9. |
[12] |
A. Greenleaf and G. Uhlmann, Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms, Ann. Inst. Fourier (Grenoble), 40 (1990), 443-466. |
[13] |
A. Greenleaf and G. Uhlmann, Microlocal techniques in integral geometry, in "Integral Geometry and Tomography" (Arcata, CA, 1989), 121-136 Contemporary Math., 113 Amer. Math. Soc., Providence, RI, 1990. |
[14] |
V. Guillemin, "Cosmology in $(2 + 1)$-Dimensions, Cyclic Models, and Deformations of $M_{2,1}$," Annals of Mathematics Studies, 121, Princeton University Press, Princeton, NJ, 1989. |
[15] |
V. Guillemin and S. Sternberg, "Geometric Asymptotics," Mathematical Surveys, No. 14, American Mathematical Society, Providence, RI, 1977. |
[16] |
V. Guillemin and G. Uhlmann, Oscillatory integrals with singular symbols, Duke Math. J., 48 (1981), 251-267.
doi: 10.1215/S0012-7094-81-04814-6. |
[17] |
L. Hörmander, Fourier integral operators, I, Acta Mathematica, 127 (1971), 79-183.
doi: 10.1007/BF02392052. |
[18] |
A. M. Horne and G. Yates, "Bistatic Synthetic Aperture Radar," Proc. IEEE Radar Conf., 2002, 6-10. |
[19] |
L. Hörmander, "The Analysis of Linear Partial Differential Operators, I-IV," Springer-Verlag, New York, 1983. |
[20] |
A. K. Louis and E. T. Quinto, Local tomographic methods in SONAR, in "Surveys on Solution Methods for Inverse Problems" (Vienna/New York) (eds. D. Colton, H. Engl, A. Louis, J. McLaughlin and W. Rundell), Springer, Vienna, 2000, 147-154. |
[21] |
R. Melrose and G. Uhlmann, Lagrangian intersection and the Cauchy problem, Comm. Pure Appl. Math., 32 (1979), 483-519. |
[22] |
C. J. Nolan and M. Cheney, Synthetic aperture inversion, Inverse Problems, 18 (2002), 221-235.
doi: 10.1088/0266-5611/18/1/315. |
[23] |
C. J. Nolan and M. Cheney, Microlocal analysis of synthetic aperture radar imaging, J. Fourier Anal. Appl., 10 (2004), 133-148.
doi: 10.1007/s00041-004-8008-0. |
[24] |
E. T. Quinto, The dependence of the generalized Radon transform on defining measures, Trans. Amer. Math. Soc., 257 (1980), 331-346.
doi: 10.1090/S0002-9947-1980-0552261-8. |
[25] |
F. Tréves, "Introduction to Pseudodifferential and Fourier Integral Operators," Vol. 1 and 2, Plenum Press, New York, 1980. |
[26] |
C. E. Yarman, B. Yazıcı and M. Cheney, Bistatic synthetic aperture radar imaging with arbitrary trajectories, IEEE Transactions on Image Processing, 17 (2008), 84-93.
doi: 10.1109/TIP.2007.911812. |
show all references
References:
[1] |
L.-E. Andersson, On the determination of a function from spherical averages, SIAM J. Math. Anal., 19 (1988), 214-232.
doi: 10.1137/0519016. |
[2] |
M. Cheney, A mathematical tutorial on synthetic aperture radar, SIAM Rev., 43 (2001), 301-312.
doi: 10.1137/S0036144500368859. |
[3] |
M. Cheney and B. Borden, "Fundamentals of Radar Imaging," CBMS-NSF Regional Conference Series in Applied Mathematics, 79, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pennsylvania, 2009. |
[4] |
J. Duistermaat, "Fourier Integral Operators," Birkhäuser Boston, Inc., Boston, Massachusetts, 1996. |
[5] |
J. Cohen and H. Bleistein, Velocity inversion procedure for acoustic waves, Geophysics, 44 (1979), 1077-1085.
doi: 10.1190/1.1440996. |
[6] |
T. Dowling, "Radar Imaging Using Multiply Scattered Waves," Ph.D. Thesis, University of Limerick, Ireland, 2009. |
[7] |
R. Felea, Composition of Fourier integral operators with fold and blowdown singularities, Comm. Partial Differential Equations, 30 (2005), 1717-1740. |
[8] |
R. Felea, Displacement of artefacts in inverse scattering, Inverse Problems, 23 (2007), 1519-1531.
doi: 10.1088/0266-5611/23/4/009. |
[9] |
R. Felea and A. Greenleaf, An FIO calculus for marine seismic imaging: Folds and cross caps, Comm. P.D.E., 33 (2008), 45-77.
doi: 10.1080/03605300701318716. |
[10] |
A. Greenleaf and G. Uhlmann, Non-local inversion formulas for the X-ray transform, Duke Math. J., 58 (1989), 205-240.
doi: 10.1215/S0012-7094-89-05811-0. |
[11] |
A. Greenleaf and G. Uhlmann, Estimates for singular Radon transforms and pseudodifferential operators with singular symbols, J. Functional Anal., 89 (1990), 202-232.
doi: 10.1016/0022-1236(90)90011-9. |
[12] |
A. Greenleaf and G. Uhlmann, Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms, Ann. Inst. Fourier (Grenoble), 40 (1990), 443-466. |
[13] |
A. Greenleaf and G. Uhlmann, Microlocal techniques in integral geometry, in "Integral Geometry and Tomography" (Arcata, CA, 1989), 121-136 Contemporary Math., 113 Amer. Math. Soc., Providence, RI, 1990. |
[14] |
V. Guillemin, "Cosmology in $(2 + 1)$-Dimensions, Cyclic Models, and Deformations of $M_{2,1}$," Annals of Mathematics Studies, 121, Princeton University Press, Princeton, NJ, 1989. |
[15] |
V. Guillemin and S. Sternberg, "Geometric Asymptotics," Mathematical Surveys, No. 14, American Mathematical Society, Providence, RI, 1977. |
[16] |
V. Guillemin and G. Uhlmann, Oscillatory integrals with singular symbols, Duke Math. J., 48 (1981), 251-267.
doi: 10.1215/S0012-7094-81-04814-6. |
[17] |
L. Hörmander, Fourier integral operators, I, Acta Mathematica, 127 (1971), 79-183.
doi: 10.1007/BF02392052. |
[18] |
A. M. Horne and G. Yates, "Bistatic Synthetic Aperture Radar," Proc. IEEE Radar Conf., 2002, 6-10. |
[19] |
L. Hörmander, "The Analysis of Linear Partial Differential Operators, I-IV," Springer-Verlag, New York, 1983. |
[20] |
A. K. Louis and E. T. Quinto, Local tomographic methods in SONAR, in "Surveys on Solution Methods for Inverse Problems" (Vienna/New York) (eds. D. Colton, H. Engl, A. Louis, J. McLaughlin and W. Rundell), Springer, Vienna, 2000, 147-154. |
[21] |
R. Melrose and G. Uhlmann, Lagrangian intersection and the Cauchy problem, Comm. Pure Appl. Math., 32 (1979), 483-519. |
[22] |
C. J. Nolan and M. Cheney, Synthetic aperture inversion, Inverse Problems, 18 (2002), 221-235.
doi: 10.1088/0266-5611/18/1/315. |
[23] |
C. J. Nolan and M. Cheney, Microlocal analysis of synthetic aperture radar imaging, J. Fourier Anal. Appl., 10 (2004), 133-148.
doi: 10.1007/s00041-004-8008-0. |
[24] |
E. T. Quinto, The dependence of the generalized Radon transform on defining measures, Trans. Amer. Math. Soc., 257 (1980), 331-346.
doi: 10.1090/S0002-9947-1980-0552261-8. |
[25] |
F. Tréves, "Introduction to Pseudodifferential and Fourier Integral Operators," Vol. 1 and 2, Plenum Press, New York, 1980. |
[26] |
C. E. Yarman, B. Yazıcı and M. Cheney, Bistatic synthetic aperture radar imaging with arbitrary trajectories, IEEE Transactions on Image Processing, 17 (2008), 84-93.
doi: 10.1109/TIP.2007.911812. |
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