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Applicable Analysis
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Volume 93, 2014 - Issue 6
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Articles

Uniqueness of two phaseless non-overdetermined inverse acoustics problems in 3-d

Pages 1135-1149 | Received 09 Apr 2013, Accepted 18 Jun 2013, Published online: 08 Jul 2013

References

  • Novikov RG. The inverse scattering problem on a fixed energy level for the two-dimensional Schrödinger operator. Journal of Functional Analysis. 1992;103:409–463.
  • Novikov RG. ∂–bar approach to approximate inverse scattering at fixed energy in three dimensions. International Mathematics Research Papers. 2005;6:287–349.
  • Klibanov MV. Phaseless inverse scattering problems in 3-d. Available online at arxiv: 1303.0923v1 [math-ph] 2013 Mar 5.
  • Romanov VG. Inverse problems of mathematical physics. Utrecht: VNU Science Press; 1986.
  • Klibanov MV. Carleman estimates for global uniqueness, stability and numerical methods for inverse problems. Journal of Inverse and Ill-Posed Problems. in press; 21. Available online of this journal as Ahead of Print. doi:10.1515/jiip-2012-0072.
  • Klibanov MV. Thermoacoustic tomography with an arbitrary elliptic operator. Inverse Problems. 2013;29:025014.
  • Bukhgeim AL, Klibanov MV. Uniqueness in the large of a class of multidimensional inverse problems. Soviet Mathematics Doklady. 1981;17:244–247.
  • Beilina L, Klibanov MV. Approximate global convergence and adaptivity for coefficient inverse problems. New York: Springer; 2012.
  • Kokurin MYu. On a multidimensional integral equation with data supported by low dimensional analytic manifodls. Journal of Inverse and Ill-Posed Problems. 2013;21:125–140.
  • Lavrent’ev MM. On an inverse problem for the wave equation. Soviet Mathematics Doklady. 1964;5:970–972.
  • Vainberg BR. Asymptotic methods in equations of mathematical physics. New York: Gordon and Breach Science; 1989.
  • Vainberg BR. Principles of radiation, limiting absorption and limiting amplitude in the general theory of partial differential equations. Russian Mathematical Surveys. 1966;21:115–193.
  • Gilbarg D, Trudinger NS. Elliptic partial differential equations of second order. New York: Springer; 1984.
  • Berk NF, Majkrzak CF. Statistical analysis of phase-inversion neutron specular reflectivity. Langmuir. 2009;25:4132–4144.
  • Ladd MFC, Palmer RA. Structure determination by X-ray crystallography. New York: Plenum Press; 1993.
  • Fienup JR, Maron JC, Schulz TJ, Seldin JH. Hubble space telescope characterization by using phase retrieval algorithms. Applied Optics. 1993;32:1747–1768.
  • Fienup JR. Phase retrieval algorithms: a personal tour [invited]. Applied Optics. 2013;52:45–56.
  • Klibanov MV, Sacks PE. Phaseless inverse scattering and the phase problem in optics. Journal of Mathematical Physics. 1992;33:3813–3821.
  • Nazarchuk ZT, Hryniv RO, Synyavskyy AT. Reconstruction of the impedance Schrödinger equation from the modulus of the reflection coefficients. Wave Motion. 2012;49:719–736.
  • Aktosun T, Sacks PE. Inverse problem on the line without phase information. Inverse Problems. 1998;14:211–224.
  • Klibanov MV, Sacks PE, Tikhonravov AV. The phase retrieval problem. Topical Review. Inverse Problems. 1995;11:1–28.
  • Klibanov MV. Determination of a function with compact support from the absolute value of its Fourier transform, and an inverse scattering problem. Differential Equations. 1987;22:1232–1240.
  • Klibanov MV. On the recovery of a 2-D function from the modulus of its Fourier transform. Journal of Mathematical Analysis and Applications. 2006;323:818–843.
  • Dobson D. Phase reconstruction via nonlinear least squares. Inverse Problems. 1992;8:541–557.
  • Hurt NE. Phase retrieval and zero crossings: mathematical methods in image reconstruction. Dodrecht: Kluwer Academic; 2002.
  • Sixou B, Davidoiu V, Langer M, Peyrin F. Absorption and phase retrieval with Tikhonov and joint sparsity regularizations. Inverse Problems and Imaging. 2013;7:267–282.
  • Dai Z, Lamm PK. Local regularization for the nonlinear autoconvolution problem. SIAM Journal on Numerical Analysis. 2008;46:832–868.
  • Gerth D, Hoffman B, Birkholz S, Koke S, Steinmeyer G. Regularization of an autoconvolution problem in ultrashort laser pulse characterization. Inverse Problems in Science and Engineering. in press. Available online of this journal as Latest Articles. doi:10.1080/17415977.2013.769535.
  • Ivanyshyn O. Shape reconstruction of acoustic obstacles from the modulus of the far field pattern. Inverse Problems and Imaging. 2007;1:609–622.
  • Ivanyshyn O, Kress R. Identification of sound-soft 3D obstacles from phaseless data. Inverse Problems and Imaging. 2010;4:131–149.
  • Alekseev GV. On the incorrectness of the non-linear operator equation of the first kind in antenna synthesis theory. USSR Computational Mathematics and Mathematical Physics. 1979;19:243–249.
  • Alekseev GV. On the theory of multi-dimensional problems of radiating system synthesis. USSR Computational Mathematics and Mathematical Physics. 1982;22:173–180.
  • Ladyzhenskaya OA. Boundary value problems of mathematical physics. New York: Springer; 1985.

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