“Fast” Solution of the Three-Dimensional Inverse Problem of Quasi-Static Elastography with the Help of the Small Parameter Method

[1] Gao L.(1996)Imaging of the elastic properties of tissue—a review Ultrasound Med. Biol. 22 959-977

[2] Parker K.(1999)Elastography: Ultrasonic estimation and imaging of the elastic properties of tissues Proc. Inst. Mech. Eng. Part H: J. Eng. Med. 213 203-233

[3] Lerner R.(2003)Selected methods for imaging elastic properties of biological tissues Annu. Rev. Biomed. Eng. 5 57-78

[4] Ophir J.(2005)A unified view of imaging the elastic properties of tissue J. Acoust. Soc. Am. 117 2705-2712

[5] Alam S.(2012)Model-based elastography: A survey of approaches to the inverse elasticity problem Phys. Med. Biol. R 57 35-73

[6] Garra B.(2003)Solution of inverse problems in elasticity imaging using the adjoint method Inverse Probl. 19 297-313

[7] Greenleaf J. F.(2009)Quantitative three-dimensional elasticity imaging from quasi-static deformation: A phantom study Phys. Med. Biol. 54 757-779

[8] Fatemi M.(2017)A posteriori error estimates for numerical solutions to inverse problems of elastography Inverse Probl. Sci. Eng. 25 114-128

[9] Insana M.(2017)Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimate J. Inverse Ill-Posed Probl. 26 1-7

[10] Parker K. J.(2021)Solution of the three-dimensional inverse elastography problem for parametric classes of inclusions Inverse Probl. Sci. Eng. 29 1055-1069

[1] Gao L.(1996)Imaging of the elastic properties of tissue—a review Ultrasound Med. Biol. 22 959-977

[2] Parker K.(1999)Elastography: Ultrasonic estimation and imaging of the elastic properties of tissues Proc. Inst. Mech. Eng. Part H: J. Eng. Med. 213 203-233

[3] Lerner R.(2003)Selected methods for imaging elastic properties of biological tissues Annu. Rev. Biomed. Eng. 5 57-78

[4] Ophir J.(2005)A unified view of imaging the elastic properties of tissue J. Acoust. Soc. Am. 117 2705-2712

[5] Alam S.(2012)Model-based elastography: A survey of approaches to the inverse elasticity problem Phys. Med. Biol. R 57 35-73

[6] Garra B.(2003)Solution of inverse problems in elasticity imaging using the adjoint method Inverse Probl. 19 297-313

[7] Greenleaf J. F.(2009)Quantitative three-dimensional elasticity imaging from quasi-static deformation: A phantom study Phys. Med. Biol. 54 757-779

[8] Fatemi M.(2017)A posteriori error estimates for numerical solutions to inverse problems of elastography Inverse Probl. Sci. Eng. 25 114-128

[9] Insana M.(2017)Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimate J. Inverse Ill-Posed Probl. 26 1-7

[10] Parker K. J.(2021)Solution of the three-dimensional inverse elastography problem for parametric classes of inclusions Inverse Probl. Sci. Eng. 29 1055-1069