A new version of the quasi-reversibility method for the thermoacoustic tomography and a coefficient inverse problem

DOI10.1080/00036810802001297zbMath1152.35515arXiv0712.0175OpenAlexW2150295535WikidataQ58289575 ScholiaQ58289575MaRDI QIDQ5503683

Dmitrii V. Nechaev, Andrey V. Kuzhuget, Michael V. Klibanov, Sergey I. Kabanikhin

Publication date: 16 January 2009

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.0175

zbMATH Keywords

numerical resultsCarleman estimatequasi-reversibility methodimaging of sharp peaks

Mathematics Subject Classification ID

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Cites Work

• Explicit inversion formulae for the spherical mean Radon transform
• Numerical solution of the problem of computational time reversal in a quadrant
• The Quasi-Reversibility Method for Thermoacoustic Tomography in a Heterogeneous Medium
• Newton-Kantorovich method for three-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time-dependent data
• A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace’s Equation
• Numerical solution of a time-like Cauchy problem for the wave equation
• Stability estimates for ill-posed cauchy problems involving hyperbolic equations and inequalities
• Determining a Function from Its Mean Values Over a Family of Spheres
• Numerical solution of 2D thermoacoustic problem
• Lipschitz stability for hyperbolic inequalities in octants with the lateral Cauchy data and refocising in time reversal
• Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation
• Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed
• A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation

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