239
Views
2
CrossRef citations to date
0
Altmetric
Articles

A wavelet multiscale-adaptive homotopy method for the inverse problem of nonlinear diffusion equation

&
Pages 617-634 | Received 16 Apr 2013, Accepted 08 May 2014, Published online: 06 Jun 2014

References

  • Goyal K, Mehra M. Wavelets and inverse problems. In: Proceedings of the Satellite Conference of ICM 2010; 2010 Aug 14–17; New Delhi, India. Singapore: World Scientific; 2010. p. 430–447.
  • Donoho DL. Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data. Proc. Symp. Appl. Math. 1993;47:173–205.
  • Donoho DL. Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal. 1995;2:101–126.
  • Daubechies I. Ten lectures on wavelets. Philadelphia (PA): SIAM; 1992.
  • Liu J. A multiresolution method for distributed parameter estimation. SIAM J. Sci. Comput. 1993;14:389–405.
  • Fu HS, Han B. A wavelet multiscale method for the inverse problems of a two-dimensional wave equation. Inverse Probl. Sci. Eng. 2004;12:643–656.
  • Fu HS, Han B, Gai GQ. A wavelet multiscale-homotopy method for the inverse problem of two-dimensional acoustic wave equation. Appl. Math. Comput. 2007;190:576–582.
  • Zhang XM, Liu KA, Liu JQ. The wavelet multiscale method for inversion of porosity in the fluid-saturated porous media. Appl. Math. Comput. 2006;180:419–427.
  • Zhang XM, Liu JQ, Liu KA. Porosity inversion of 1-D two-phase medium with wavelet multiscale method. Acta Phys. Sin. 2008;57:654–660.
  • Zhang XM, Zhou CY, Liu JQ, Liu KA. Multiparameter identification of fluid-saturated porous medium with the wavelet multiscale method. J. Porous Media. 2009;12:255–264.
  • He Y, Han B. A wavelet adaptive-homotopy method for inverse problem in the fluid-saturated porous media. Appl. Math. Comput. 2009;208:189–196.
  • Ding L, Han B, Liu JQ. A wavelet multiscale method for inversion of Maxwell equations. Appl. Math. Mech. -Engl. Ed. 2009;30:1035–1044.
  • Watson LT. Globally convergent homotopy methods: a tutorial. Appl. Math. Comput. 1989;31:369–396.
  • Tian YC, Zhang ZM, Ma JW, Yang HZ. Inversing physical parameter of two-phase viscoelastic media by homotopy method. Chin. J. Geophys. -Chinese Ed. 2009;52:2328–2334.
  • Han B, Shao JQ, Guo BQ. A widely convergent method for determining the distributed parameters of an elliptical equation. Appl. Math. Comput. 1994;60:139–146.
  • Han B, Feng GF, Liu JQ. A widely convergent generalized pulse-spectrum technique for the inversion of two-dimensional acoustic wave equation. Appl. Math. Comput. 2006;172:406–420.
  • Han B, Fu HS, Li Z. A homotopy method for the inversion of a two-dimensional acoustic wave equation. Inverse Probl. Sci. Eng. 2005;13:411–431.
  • Han B, Fu HS, Liu H. a homotopy method for well-log constraint waveform inversion. Geophysics. 2007;72:R1–R7.
  • Fu HS, Han B. A regularization homotopy method for the inverse problem of 2-D wave equation and well log constraint inversion. Chin. J. Geophys. -Chinese Ed. 2005;48:1441–1448.
  • Feng GF, Han B, Liu JQ. Widely convergent generalized pulse-spectrum methods for 2-D wave equation inversion. Chin. J. Geophys. -Chinese Ed. 2003;46:265–270.
  • Dou YX, Han B. Numerical inversion of reconstruction of mountain surface by homotopy method. Chin. J. Geophys. -Chinese Ed. 2011;54:1893–1899.
  • Hu JL, Hirasawa K, Kumamaru K. A homotopy approach to improving PEM identification of ARMAX models. Automatica. 2001;37:1323–1334.
  • Zhao JJ, Liu T, Liu SS. Identification of space-dependent permeability in nonlinear diffusion equation from interior measurements using wavelet multiscale method. Inverse Probl. Sci. Eng. 2014;22:507–529.
  • Zhao JJ, Liu T, Liu SS. An adaptive homotopy method for permeability estimation of a nonlinear diffusion equation. Inverse Probl. Sci. Eng. 2013;21:585–604.
  • Tarantola A. Inverse problem theory and methods for model parameter estimation. Philadelphia (PA): SIAM; 2005.
  • Aster RC, Borchers B, Thurber CH. Parameter estimation and inverse problems. Boston: Elsevier; 2005.
  • Cohen A, Daubechies I, Feauveau JC. Biorthogonal bases of compactly supported wavelets. Commun. Pure Appl. Math. 1992;45:485–560.
  • Mallat SG. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 1989;11:674–693.
  • Nilssen TK, Mannseth T, Tai XC. Permeability estimation with the augmented Lagrangian method for a nonlinear diffusion equation. Comput. Geosci. 2003;7:27–47.
  • Azzalini A, Farge M, Schneider K. Nonlinear wavelet thresholding: a recursive method to determine the optimal denoising threshold. Appl. Comput. Harmon. Anal. 2005;18:177–185.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.