@article{RM_2016_71_3_a2,
author = {V. P. Palamodov},
title = {New approaches to inverse scattering},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {513--537},
year = {2016},
volume = {71},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/RM_2016_71_3_a2/}
}
V. P. Palamodov. New approaches to inverse scattering. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 71 (2016) no. 3, pp. 513-537. http://geodesic.mathdoc.fr/item/RM_2016_71_3_a2/
[1] A. M. Cormack, “A paraboloidal Radon transform”, 75 years of Radon transform (Vienna, 1992), Conf. Proc. Lecture Notes Math. Phys., IV, Int. Press, Cambridge, MA, 1994, 105–109 | MR | Zbl
[2] A. M. Cormack, “The Radon transform on a family of curves in the plane”, Proc. Amer. Math. Soc., 83:2 (1981), 325–330 ; “II”, 86:2 (1982), 293–298 | DOI | MR | Zbl | DOI | MR | Zbl
[3] A. M. Cormack, “Radon's problem – old and new”, Inverse problems (New York, 1983), SIAM-AMS Proc., 14, Amer. Math. Soc., Providence, RI, 1984, 33–39 | MR | Zbl
[4] A. M. Cormack, “Radon's problem for some surfaces in $\mathbf {R}^{n}$”, Proc. Amer. Math. Soc., 99:2 (1987), 305–312 | DOI | MR | Zbl
[5] V. P. Palamodov, “A uniform reconstruction formula in integral geometry”, Inverse Problems, 28:6 (2012), 065014, 15 pp. | DOI | MR | Zbl
[6] V. P. Palamodov, Reconstruction from integral data, Monogr. Res. Notes Math., CRC Press, Boca Raton, FL, 2016, 194 pp. | Zbl
[7] S. J. Norton, “Compton scattering tomography”, J. Appl. Phys., 76:4 (1994), 2007–2015 | DOI
[8] M. K. Nguyen, T. T. Truong, “Inversion of a new circular-arc Radon transform for Compton scattering tomography”, Inverse Problems, 26:6 (2010), 065005, 13 pp. | DOI | MR | Zbl
[9] S. Helgason, “Differential operators on homogeneous spaces”, Acta Math., 102:3 (1959), 239–299 | DOI | MR | Zbl
[10] I. M. Gel'fand, M. I. Graev, N. Ya. Vilenkin, Generalized functons, v. 5, Integral geometry and representation theory, Academic Press, New York–London, 1966, xvii+449 pp. | MR | MR | Zbl | Zbl
[11] A. M. Korsunsky, W. J. J. Vorster, S. Y. Zhang, D. Dini, D. Latham, M. Golshan, J. Liu, Y. Kyriakoglou, M. J. Walsh, “The principle of strain reconstruction tomography: determination of quench strain distribution from diffraction measurements”, Acta Materialia, 54:8 (2006), 2101–2108 | DOI
[12] V. A. Sharafutdinov, Integral geometry for tensor fields, Inverse Ill-posed Probl. Ser., VSP, Utrecht, 1994, 271 pp. | DOI | MR | MR | Zbl | Zbl
[13] V. A. Sharafutdinov, “Slice-by-slice reconstruction algorithm for vector tomography with incomplete data”, Inverse Problems, 23:6 (2007), 2603–2627 | DOI | MR | Zbl
[14] A. Denisjuk, “Inversion of the x-ray transform for 3D symmetric tensor fields with sources on a curve”, Inverse Problems, 22:2 (2006), 399–411 | DOI | MR | Zbl
[15] V. Palamodov, “On reconstruction of strain fields from tomographic data”, Inverse Problems, 31:8 (2015), 85002, 12 pp. | DOI | MR | Zbl
[16] F. Natterer, F. Wübbeling, Mathematical methods in image reconstruction, SIAM Monogr. Math. Model. Comput., SIAM, Philadelphia, PA, 2001, xii+216 pp. | DOI | MR | Zbl
[17] V. P. Palamodov, “Stability in diffraction tomography and a nonlinear ‘basic theorem’\kern1pt”, J. Anal. Math., 91 (2003), 247–268 | DOI | MR | Zbl
[18] H. Ammari, H. Bahouri, D. Dos Santos Ferreira, I. Gallagher, “Stability estimates for an inverse scattering problem at high frequencies”, J. Math. Anal. Appl., 400:2 (2013), 525–540 | DOI | MR | Zbl
[19] J. Sylvester, G. Uhlmann, “A global uniqueness theorem for an inverse boundary value problem”, Ann. of Math. (2), 125:1 (1987), 153–169 | DOI | MR | Zbl
[20] R. G. Novikov, “Multidimensional inverse spectral problems for the equation $-\Delta\psi+(v(x)-Eu(x))\psi=0$”, Funct. Anal. Appl., 22:4 (1988), 263–272 | DOI | MR | Zbl
[21] A. I. Nachman, “Reconstructions from boundary measurements”, Ann. of Math. (2), 128:3 (1988), 531–576 | DOI | MR | Zbl
[22] G. Eskin, J. Ralston, “The inverse backscattering problem in three dimensions”, Comm. Math. Phys., 124:2 (1989), 169–215 | DOI | MR | Zbl
[23] G. Uhlmann, “Developments in inverse problems since Calderón's foundational paper”, Harmonic analysis and partial differential equations (Chicago, IL, 1996), Chicago Lectures in Math., Univ. Chicago Press, Chicago, IL, 1999, 295–345 | MR | Zbl
[24] P. Stefanov, “Stability of the inverse problem in potential scattering at fixed energy”, Ann. Inst. Fourier (Grenoble), 40:4 (1990), 867–884 | DOI | MR | Zbl
[25] M. Born, E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light, 7th ed., Cambridge Univ. Press, Cambridge, 1999, 985 pp. | MR | Zbl
[26] J. P. Klauder, B. S. Skagerstam (eds.), Coherent states. Applications in physics and mathematical physics, World Scientific Publishing Co., Singapore, 1985, xviii+911 pp. | DOI | MR | Zbl
[27] M. A. Leontovich, “Ob odnom metode resheniya zadach o rasprostranenii elektromagnitnykh voln vdol poverkhnosti zemli”, Izv. AN SSSR. Ser. fiz., 8:1 (1944), 16–22 | MR | Zbl
[28] V. A. Fock, “The field of a plane wave near the surface of a conducting body”, Acad. Sci. USSR. J. Phys., 10 (1946), 399–409 | MR | MR | Zbl
[29] V. M. Babič, V. S. Buldyrev, Short-wavelength diffraction theory. Asymptotic methods, Springer Ser. Wave Phenomena, 4, Springer-Verlag, Berlin, 1991, xi+445 pp. | MR | MR | Zbl | Zbl
[30] V. M. Babich, “The construction of Gaussian beams with exponentially small residual”, J. Math. Sci., 79:4 (1996), 1169–1171 | DOI | MR | Zbl
[31] A. E. Siegman, Lasers, Univ. Sci. Books, Sausalito, CA, 1986, 1283 pp.
[32] O. Svelto, Principles of lasers, 5th ed., Springer, Heidelberg, 2010, xxii+620 pp. | DOI
[33] A. E. Siegman, “How to (maybe) measure laser beam quality”, DPSS lasers: applications and issues, Tutorial presentation at the Optical Society of America Annual Meeting Long Beach, OSA Trends in Optics and Photonics, 17, OSA, Washington, DC, 1998, MQ1 | DOI
[34] S. Novikov, S. V. Manakov, L. P. Pitaevskiĭ, V. E. Zakharov, Theory of solitons. The inverse scattering method, Contemp. Soviet Math., Consultants Bureau [Plenum], New York, 1984, xi+286 pp. | MR | MR | Zbl | Zbl
[35] F. Natterer, “Reflectors in wave equation imaging”, Wave Motion, 45:6 (2008), 776–784 | DOI | MR | Zbl
[36] C. Prada, S. Manneville, D. Spoliansky, M. Fink, “Decomposition of the time-reversal operator: detection and selective focusing on two scatterers”, J. Acoust. Soc. Amer., 99:4 (1996), 2067–2076 | DOI
[37] M. Fink, C. Prada, “Acoustic time-reversal mirrors”, Inverse Problems, 17:1 (2001), R1–R38 | DOI | Zbl
[38] I. Petrowsky, “On the diffusion of waves and the lacunas for hyperbolic equations”, Matem. sb., 17(59):3 (1945), 289–370 | MR | Zbl
[39] V. I. Arnold, “On the Newtonian potential of hyperbolic layers”, Selecta Math. Sov., 4:1 (1985), 103–106 | MR | Zbl
[40] V. P. Palamodov, “Time reversal in photoacoustic tomography and levitation in a cavity”, Inverse Problems, 30:12 (2014), 125006, 16 pp. | DOI | MR | Zbl
[41] A. L. Bukhgeim, V. B. Kardakov, “Solution of the inverse problem for the equation of elastic waves by the method of spherical means”, Sib. Math. J., 19 (1979), 528–535 | DOI | Zbl
[42] E. K. Narayanan, Rakesh, “Spherical means with centers on a hyperplane in even dimensions”, Inverse Problems, 26:3 (2010), 035014, 12 pp. | DOI | MR | Zbl