Mathematics of thermoacoustic tomography
From MaRDI portal
Publication:3503196
DOI10.1017/S0956792508007353zbMath1185.35327arXiv0704.0286MaRDI QIDQ3503196
Leonid A. Kunyansky, Peter A. Kuchment
Publication date: 22 May 2008
Published in: European Journal of Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0704.0286
Related Items (only showing first 100 items - show all)
The Radon Transform over Cones with Vertices on the Sphere and Orthogonal Axes ⋮ Singular Value Decomposition of the Wave Forward Operator with Radial Variable Coefficients ⋮ Identification of an unknown spatial source function in a multidimensional hyperbolic partial differential equation with interior degeneracy ⋮ Weighted Radon transforms of vector fields, with applications to magnetoacoustoelectric tomography ⋮ Reconstructing the initial state of the linear system and estimating its error in discretization ⋮ Fixed Angle Inverse Scattering for Sound Speeds Close to Constant ⋮ Simultaneous Reconstruction of Optical and Acoustical Properties in Photoacoustic Imaging Using Plasmonics ⋮ Some results on the regional reconstruction of semilinear sub-diffusion fractional processes ⋮ Microlocal analysis for spherical Radon transform: two nonstandard problems ⋮ Reconstructions in ultrasound modulated optical tomography ⋮ An Inverse Source Problem for the Elastic Wave in the Lower Half-Space ⋮ On Artifacts in Limited Data Spherical Radon Transform: Flat Observation Surfaces ⋮ On Learned Operator Correction in Inverse Problems ⋮ Multiscale Factorization of the Wave Equation with Application to Compressed Sensing Photoacoustic Tomography ⋮ Compressed Sensing Photoacoustic Tomography Reduces to Compressed Sensing for Undersampled Fourier Measurements ⋮ On the exactness of the universal backprojection formula for the spherical means Radon transform ⋮ Range description for a spherical mean transform on spaces of constant curvature ⋮ Analysis for Full-Field Photoacoustic Tomography with Variable Sound Speed ⋮ Approximate inversion of discrete Fourier integral operators ⋮ Inversion formula for a Radon-type transform arising in photoacoustic tomography with circular integrating detectors ⋮ Analytical reconstruction formula for \(n\)-dimensional conical Radon transform ⋮ Theoretically exact photoacoustic reconstruction from spatially and temporally reduced data ⋮ Recovering functions from the spherical mean transform with limited radii data by expansion into spherical harmonics ⋮ A Novel Compressed Sensing Scheme for Photoacoustic Tomography ⋮ Leon Ehrenpreis, Recollections from the Recent Decades ⋮ Mathematics of Hybrid Imaging: A Brief Review ⋮ Analysis of the Magnetoacoustic Tomography with Magnetic Induction ⋮ A Radon-type transform arising in photoacoustic tomography with circular detectors: spherical geometry ⋮ Efficient Inclusion of Total Variation Type Priors in Quantitative Photoacoustic Tomography ⋮ Inverse transport problems in quantitative PAT for molecular imaging ⋮ A Dissipative Time Reversal Technique for Photoacoustic Tomography in a Cavity ⋮ Enforcing Local Non-Zero Constraints in PDEs and Applications to Hybrid Imaging Problems ⋮ Computational inverse problems. Abstracts from the workshop held October 21--27, 2012. ⋮ Inverse Transport and Diffusion Problems in Photoacoustic Imaging with Nonlinear Absorption ⋮ Recovery of a Lamé parameter from displacement fields in nonlinear elasticity models ⋮ Method of analytic continuation for the inverse spherical mean transform in constant curvature spaces ⋮ Compton camera imaging and the cone transform: a brief overview ⋮ Quantitative photoacoustic imaging in the acoustic regime using SPIM ⋮ Image reconstruction from radially incomplete spherical Radon data ⋮ Recovering the initial state of an infinite-dimensional system using observers ⋮ Reconstruction of the initial state from the data measured on a sphere for plasma-acoustic wave equations ⋮ AIR tools II: algebraic iterative reconstruction methods, improved implementation ⋮ Mathematical modeling of the photoacoustic effect generated by the heating of metallic nanoparticles ⋮ Quantitative thermoacoustic tomography with microwaves sources ⋮ Texture generation for photoacoustic elastography ⋮ Stability analysis in magnetic resonance elastography. II. ⋮ An inverse spectral analysis of transmission problem in thermo- and photo-acoustic tomography ⋮ Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator ⋮ Uniqueness for a seismic inverse source problem modeling a subsonic rupture ⋮ On the convergence of the time reversal method for thermoacoustic tomography in elastic media ⋮ Inverse Transport and Acousto-Optic Imaging ⋮ Time reversal method with stabilizing boundary conditions for Photoacoustic tomography ⋮ Well-Posedness for Photoacoustic Tomography with Fabry--Perot Sensors ⋮ Range conditions for a spherical mean transform and global extendibility of solutions of the Darboux equation ⋮ Determining anisotropic conductivity using diffusion tensor imaging data in magneto-acoustic tomography with magnetic induction ⋮ NETT: solving inverse problems with deep neural networks ⋮ Direct algorithm for reconstructing small absorbers in thermoacoustic tomography problem from a single data ⋮ Identifiability of electrical and heat transfer parameters using coupled boundary measurements ⋮ Analysis of the Linearized Problem of Quantitative Photoacoustic Tomography ⋮ Nonlinear Quantitative Photoacoustic Tomography with Two-Photon Absorption ⋮ Reconstruction formula for photoacoustic tomography with cylindrical detectors ⋮ Boundary control of elliptic solutions to enforce local constraints ⋮ Reconstruction formulas for photoacoustic imaging in attenuating media ⋮ Reconstructions for some coupled-physics inverse problems ⋮ Exterior/interior problem for the circular means transform with applications to intravascular imaging ⋮ Characterizing Impacts of Model Uncertainties in Quantitative Photoacoustics ⋮ Asymptotic Expansions for Higher Order Elliptic Equations with an Application to Quantitative Photoacoustic Tomography ⋮ Reconstructing initial data using observers: Error analysis of the semi-discrete and fully discrete approximations ⋮ An inverse backward problem for degenerate two-dimensional parabolic equation ⋮ On steepest-descent-Kaczmarz methods for regularizing systems of nonlinear ill-posed equations ⋮ Mathematical analysis of the photo-acoustic imaging modality using resonating dielectric nano-particles: the \(2D\) TM-model ⋮ A linear state space model for photoacoustic imaging in an acoustic attenuating media ⋮ Numerical inversion and uniqueness of a spherical Radon transform restricted with a fixed angular span ⋮ Photoacoustic tomography with spatially varying compressibility and density ⋮ Applications of CGO solutions to coupled-physics inverse problems ⋮ Uniqueness for time-dependent inverse problems with single dynamical data ⋮ On a reconstruction formula for spherical Radon transform: a microlocal analytic point of view ⋮ Exact reconstruction in photoacoustic tomography with circular integrating detectors II: Spherical geometry ⋮ Photoacoustic tomography with line detector: exact inversion formula ⋮ Reconstruction from circular and spherical mean data ⋮ On artifacts in limited data spherical Radon transform: curved observation surface ⋮ Integral Geometry and Mathematical Problems of Image Reconstruction ⋮ Expansion Methods ⋮ Photoacoustic and Thermoacoustic Tomography: Image Formation Principles ⋮ Mathematics of Photoacoustic and Thermoacoustic Tomography ⋮ Singular values of the attenuated photoacoustic imaging operator ⋮ Inversion of the x-ray transform for complexes of lines in ${{\mathbb{R}}}^{n}$ ⋮ State reconstruction of the wave equation with general viscosity and non-collocated observation and control ⋮ Ultrasound Modulated Bioluminescence Tomography and Controllability of the Radiative Transport Equation ⋮ Causality analysis of frequency-dependent wave attenuation ⋮ A global stability estimate for the photo-acoustic inverse problem in layered media ⋮ Space time stabilized finite element methods for a unique continuation problem subject to the wave equation ⋮ To local reconstruction from the spherical mean Radon transform ⋮ A finite element data assimilation method for the wave equation ⋮ Determining both the source of a wave and its speed in a medium from boundary measurements ⋮ Operator learning approach for the limited view problem in photoacoustic tomography ⋮ Orthogonal function series formulas for inversion of the spherical Radon transform ⋮ Recovery of pressure and wave speed for photoacoustic imaging under a condition of relative uncertainty ⋮ Photoacoustic Imaging for Attenuating Acoustic Media ⋮ Attenuation Models in Photoacoustics
Cites Work
- Unnamed Item
- Unnamed Item
- Integral geometry in affine and projective spaces
- Reconstructing singularities of a function from its Radon transform
- Fundamentality of ridge functions
- Approximation by spherical waves in \(L^p\)-spaces
- Injectivity of the spherical means operator
- Image restoration in optical-acoustic tomography
- Geometry of stationary sets for the wave equation in \(\mathbb R^n\): the case of finitely supported initial data
- Ranges and inversion formulas for spherical mean operator and its dual
- Injectivity sets for the Radon transform over circles and complete systems of radial functions
- Reconstruction from limited data of arc means
- Range descriptions for the spherical mean Radon transform
- Über eine Mittelwertseigenschaft von Lösungen homogener linearer partieller Differentialgleichungen 2. Ordnung mit konstanten Koeffizienten
- Singularities of the X-Ray Transform and Limited Data Tomography in $\mathbb{R}^2 $ and $\mathbb{R}^3 $
- Explicit inversion formulae for the spherical mean Radon transform
- A Range Description for the Planar Circular Radon Transform
- The Quasi-Reversibility Method for Thermoacoustic Tomography in a Heterogeneous Medium
- The inversion problem and applications of the generalized radon transform
- Inversion ofN-Dimensional Spherical Averages
- On the Determination of a Function from Spherical Averages
- Reconstruction of a two-dimensional reflecting medium over a circular domain: Exact solution
- The Dependence of the Generalized Radon Transform on Defining Measures
- ON THE SHORT WAVE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF STATIONARY PROBLEMS AND THE ASYMPTOTIC BEHAVIOUR ASt→ ∞ OF SOLUTIONS OF NON-STATIONARY PROBLEMS
- Conical Uniqueness Sets for the Spherical Radon Transform
- Synthetic aperture inversion
- On the range characterization for the two-dimensional attenuated x-ray transformation
- Determining a Function from Its Mean Values Over a Family of Spheres
- Thermoacoustic computed tomography with large planar receivers
- On the injectivity of the circular Radon transform
- Stationary sets for the wave equation in crystallographic domains
- On local tomography
- On a Regularization Scheme for Linear Operators in Distribution Spaces with an Application to the Spherical Radon Transform
- Inversion of Spherical Means and the Wave Equation in Even Dimensions
- Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed
- Guest Editors' introduction
- A series solution and a fast algorithm for the inversion of the spherical mean Radon transform
- Application of inverse source concepts to photoacoustic tomography
- The spherical mean value operator with centers on a sphere
- Photoacoustic tomography with a limited-aperture planar sensor and a reverberant cavity
- Effects of wavelength-dependent fluence attenuation on the noninvasive photoacoustic imaging of hemoglobin oxygen saturation in subcutaneous vasculature in vivo
- Integral geometry of tensor fields on a class of non-simple Riemannian manifolds
- The range of the spherical mean value operator for functions supported in a ball
- The Level Curves of Harmonic Functions
- Filtered backprojection for thermoacoustic computed tomography in spherical geometry
This page was built for publication: Mathematics of thermoacoustic tomography