On the convergence of the time reversal method for thermoacoustic tomography in elastic media

Abstract In this article, we consider the inverse source problem arising in thermo/photo-acoustic tomography in elastic media. We show that the time reversal method, proposed by Tittelfitz (2012), converges with the sharp observation time without any constraint on the speeds of the longitudinal and shear waves.

[1]  Gunther Uhlmann,et al.  Propagation of polarization in elastodynamics with residual stress and travel times , 2002 .

[2]  Justin Tittelfitz.  Thermoacoustic tomography in elastic media , 2011, 1105.0898.

[3]  Lizabeth V. Rachele.  An Inverse Problem in Elastodynamics: Uniqueness of the Wave Speeds in the Interior , 2000 .

[4]  Michael E. Taylor,et al.  Propagation, reflection, and diffraction of singularities of solutions to wave equations , 1978 .

[5]  Maarten V. de Hoop,et al.  Decoupling of Modes for the Elastic Wave Equation in Media of Limited Smoothness , 2011 .

[6]  Justin Tittelfitz.  An Inverse Source Problem for the Elastic Wave in the Lower Half-Space , 2015, SIAM J. Appl. Math..

[7]  Unique continuation for the elastic transversely isotropic dynamical systems and its application , 2008 .

[8]  Peter Kuchment,et al.  The Radon Transform and Medical Imaging , 2014, CBMS-NSF regional conference series in applied mathematics.

[9]  C. Bardos,et al.  Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary , 1992 .

[10]  Christiaan C. Stolk,et al.  On the modeling and inversion of seismic data , 2000 .

[11]  N. Dencker.  On the propagation of polarization sets for systems of real principal type , 1982 .

[12]  Rakesh,et al.  Determining a Function from Its Mean Values Over a Family of Spheres , 2004, SIAM J. Math. Anal..

[13]  O. Oleinik,et al.  Boundary-value problems for the system of elasticity theory in unbounded domains. Korn's inequalities , 1988 .

[14]  Linh V. Nguyen,et al.  Analysis of Iterative Methods in Photoacoustic Tomography with Variable Sound Speed , 2016, SIAM J. Imaging Sci..

[15]  Linh V. Nguyen,et al.  Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media , 2008 .

[16]  Plamen Stefanov,et al.  Thermoacoustic tomography arising in brain imaging , 2010, 1009.1687.

[17]  P. Kuchment,et al.  Mathematics of thermoacoustic tomography , 2007, European Journal of Applied Mathematics.

[18]  G. Uhlmann,et al.  Thermoacoustic tomography with variable sound speed , 2009, 0902.1973.

[19]  Lauri Oksanen,et al.  Time reversal method with stabilizing boundary conditions for Photoacoustic tomography , 2016, 1605.07817.

[20]  Hongkai Zhao,et al.  An Efficient Neumann Series-Based Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed , 2011, SIAM J. Imaging Sci..