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Mathematics of Hybrid Imaging: A Brief Review (Q2905004)

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Language	Label	Description	Also known as
English	Mathematics of Hybrid Imaging: A Brief Review	scientific article

Statements

scholarly article

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Mathematics of Hybrid Imaging: A Brief Review (English)

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The Mathematical Legacy of Leon Ehrenpreis

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publication date

24 August 2012

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full work available at URL

https://arxiv.org/abs/1107.2447

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zbMATH Keywords

hybrid imaging

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computer tomography

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medical imaging

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reconstruction methods

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inverse problem

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wave equation

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multi-physics

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multi-wave

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Peter A. Kuchment

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MaRDI profile type

MaRDI publication profile

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Range conditions for a spherical mean transform

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Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed

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Range descriptions for the spherical mean Radon transform

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Range conditions for a spherical mean transform and global extendibility of solutions of the Darboux equation

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Injectivity sets for the Radon transform over circles and complete systems of radial functions

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Range conditions for the exponential Radon transform

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Reconstructions in ultrasound modulated optical tomography

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A Range Description for the Planar Circular Radon Transform

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An introduction to mathematics of emerging biomedical imaging

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Electrical Impedance Tomography by Elastic Deformation

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Mathematical Modeling in Photoacoustic Imaging of Small Absorbers

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Calderón's inverse conductivity problem in the plane

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Hybrid inverse problems and internal functionals

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Cauchy problem for ultrasound-modulated EIT

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Inverse diffusion from knowledge of power densities

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Tomography and Inverse Transport Theory

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Combined source and attenuation reconstructions in SPECT

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Inverse transport theory of photoacoustics

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Multi-source quantitative photoacoustic tomography in a diffusive regime

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Non-uniqueness result for a hybrid inverse problem

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Quantitative thermo-acoustics and related problems

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Inverse diffusion theory of photoacoustics

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The inversion problem and applications of the generalized radon transform

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Electrical impedance tomography

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Inverse gravimetry approach to attenuated tomography

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Local energy decay of the wave equation in an exterior problem and without resonance in the neighborhood of the real line

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The Existence of an Infinite Discrete Set of Transmission Eigenvalues

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Imaging by Modification: Numerical Reconstruction of Local Conductivities from Corresponding Power Density Measurements

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A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction

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A Mathematical Tutorial on Synthetic Aperture Radar

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Electrical Impedance Tomography

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Inverse acoustic and electromagnetic scattering theory.

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The interior transmission problem

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Multiple illumination quantitative photoacoustic tomography using transport and diffusion models

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Partial differential equations I. Foundations of the classical theory. Transl. from the Russian by R. Cooke

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Inversion of Spherical Means and the Wave Equation in Even Dimensions

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Determining a Function from Its Mean Values Over a Family of Spheres

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The spherical mean value operator with centers on a sphere

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The range of the spherical mean value operator for functions supported in a ball

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Impedance-Acoustic Tomography

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The Radon transform

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Time reversal in thermoacoustic tomography—an error estimate

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Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media

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Partial differential equations

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The Calderón problem with partial data

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On the existence of transmission eigenvalues

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Mathematics of thermoacoustic tomography

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Synthetic focusing in ultrasound modulated tomography

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2D and 3D reconstructions in acousto-electric tomography

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Mathematics of Photoacoustic and Thermoacoustic Tomography

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Stabilizing inverse problems by internal data

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On local tomography

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Explicit inversion formulae for the spherical mean Radon transform

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A series solution and a fast algorithm for the inversion of the spherical mean Radon transform

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Thermoacoustic tomography with detectors on an open curve: an efficient reconstruction algorithm

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Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra

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Fundamentality of ridge functions

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Unique identifiability of elastic parameters from time-dependent interior displacement measurement

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Global uniqueness for a two-dimensional inverse boundary value problem

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Conductivity imaging with a single measurement of boundary and interior data

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Recovering the conductivity from a single measurement of interior data

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Current density impedance imaging

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Mathematical Methods in Image Reconstruction

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A family of inversion formulas in thermoacoustic tomography

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On singularities and instability of reconstruction in thermoacoustic tomography

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Transmission Eigenvalues

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Remarks on the general Funk transform and thermoacoustic tomography

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Guest Editors' introduction

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A parametrix for a problem of optical-acoustic tomography

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Image restoration in optical-acoustic tomography

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An Efficient Neumann Series–Based Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed

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Singularities of the X-Ray Transform and Limited Data Tomography in $\mathbb{R}^2 $ and $\mathbb{R}^3 $

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Solutions of the wave equation with localized energy

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On multi-spectral quantitative photoacoustic tomography in diffusive regime

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Magnetic Resonance Electrical Impedance Tomography (MREIT)

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Integral geometry of tensor fields on a class of non-simple Riemannian manifolds

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Thermoacoustic tomography with variable sound speed

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Thermoacoustic tomography arising in brain imaging

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Discreteness of Transmission Eigenvalues via Upper Triangular Compact Operators

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A global uniqueness theorem for an inverse boundary value problem

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ON THE SHORT WAVE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF STATIONARY PROBLEMS AND THE ASYMPTOTIC BEHAVIOUR AS<i>t</i>→ ∞ OF SOLUTIONS OF NON-STATIONARY PROBLEMS

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Photoacoustic and Thermoacoustic Tomography: Image Formation Principles

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Identifiers

zbMATH Open document ID

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10.1007/978-88-470-1947-8_12

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2905004

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