Nonlinear Ultrasound Imaging Modeled by a Westervelt Equation

DOI10.1137/21M1431813zbMath1486.35458arXiv2105.05423OpenAlexW4221044685MaRDI QIDQ5065489

Gunther Uhlmann, Jian Zhai, Sebastian Acosta

Publication date: 22 March 2022

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.05423

zbMATH Keywords

Gaussian beamsultrasound imagingnonlinear acoustic wavesWestervelt equation

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Biomedical imaging and signal processing (92C55) Inverse problems for PDEs (35R30) Second-order quasilinear hyperbolic equations (35L72)

Related Items (6)

An Inverse Boundary Value Problem Arising in Nonlinear Acoustics ⋮ An inverse problem for a semi-linear wave equation: a numerical study ⋮ On the simultaneous reconstruction of the nonlinearity coefficient and the sound speed in the Westervelt equation ⋮ Nonlinearity parameter imaging in the frequency domain ⋮ Weakly Nonlinear Geometric Optics for the Westervelt Equation and Recovery of the Nonlinearity ⋮ On inverse problems for a strongly damped wave equation on compact manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• The Calderón problem in transversally anisotropic geometries
• Energy methods for quasilinear hyperbolic initial-boundary value problems. Applications to elastodynamics
• Bayliss-Turkel-like radiation conditions on surfaces of arbitrary shape
• Boundary control and quasiphotons in the problem of reconstruction of a Riemannian manifold via dynamical data
• Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations
• On an inverse boundary value problem for a nonlinear elastic wave equation
• Inverse boundary value problems for wave equations with quadratic nonlinearities
• Recovery of time-dependent coefficients from boundary data for hyperbolic equations
• An inverse problem for a semi-linear elliptic equation in Riemannian geometries
• Inverse problems for nonlinear hyperbolic equations
• Nonlinear interaction of waves in elastodynamics and an inverse problem
• High order surface radiation conditions for time-harmonic waves in exterior domains
• The inverse problem for the local geodesic ray transform
• The Mathematics of Computerized Tomography
• Sensitivity analysis of an inverse problem for the wave equation with caustics
• Geometrization of the Leading Term in Acoustic Gaussian Beams
• Parabolic Wave Equation Approximations in Heterogenous Media
• Higher Order Paraxial Wave Equation Approximations in Heterogeneous Media
• Nucleation and mean curvature flow
• Inverse problems for nonlinear hyperbolic equations with disjoint sources and receivers
• RECOVERY OF ZEROTH ORDER COEFFICIENTS IN NON-LINEAR WAVE EQUATIONS
• An Inverse Boundary Value Problem for a Semilinear Wave Equation on Lorentzian Manifolds
• Determination of Space‐Time Structures from Gravitational Perturbations
• The geodesic X-ray transform with matrix weights
• The Mathematics of Medical Imaging

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