Image reconstruction from radially incomplete spherical Radon data
From MaRDI portal
Publication:4575289
DOI10.1017/S0956792517000250zbMath1392.94032arXiv1702.04784MaRDI QIDQ4575289
Rim Gouia-Zarrad, Venkateswaran P. Krishnan, Souvik Roy, Gaik Ambartsoumian
Publication date: 13 July 2018
Published in: European Journal of Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1702.04784
medical imagingspherical harmonicstruncated singular value decompositionVolterra integral equationsspherical Radon transform
Image processing (compression, reconstruction, etc.) in information and communication theory (94A08)
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Cites Work
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- Method of analytic continuation for the inverse spherical mean transform in constant curvature spaces
- The regularizing properties of the composite trapezoidal method for weakly singular Volterra integral equations of the first kind
- The truncated SVD as a method for regularization
- Fundamentality of ridge functions
- Approximation by spherical waves in \(L^p\)-spaces
- Geometry of stationary sets for the wave equation in \(\mathbb R^n\): the case of finitely supported initial data
- Spherical harmonic analysis and synthesis for global multiresolution applications
- On the expansion of a function in terms of spherical harmonics in arbitrary dimensions
- Injectivity sets for the Radon transform over circles and complete systems of radial functions
- An inversion formula for the spherical mean transform with data on an ellipsoid in two and three dimensions
- A family of inversion formulas in thermoacoustic tomography
- An efficient numerical algorithm for the inversion of an integral transform arising in ultrasound imaging
- Range descriptions for the spherical mean Radon transform
- Thermoacoustic tomography arising in brain imaging
- Inversion of the circular Radon transform on an annulus
- Inversion of a Class of Circular and Elliptical Radon Transforms
- Explicit inversion formulae for the spherical mean Radon transform
- A Range Description for the Planar Circular Radon Transform
- Mathematics of thermoacoustic tomography
- Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media
- Fundamentals of Radar Imaging
- On the Determination of a Function from Spherical Averages
- Reconstruction of a two-dimensional reflecting medium over a circular domain: Exact solution
- A Multigrid Tutorial, Second Edition
- Determining a Function from Its Mean Values Over a Family of Spheres
- On the injectivity of the circular Radon transform
- Thermoacoustic tomography with variable sound speed
- Inversion of Spherical Means and the Wave Equation in Even Dimensions
- Universal Inversion Formulas for Recovering a Function from Spherical Means
- A series solution and a fast algorithm for the inversion of the spherical mean Radon transform
- The spherical mean value operator with centers on a sphere
- Inversion formulae for the spherical mean in odd dimensions and the Euler–Poisson–Darboux equation
- Calculating the Singular Values and Pseudo-Inverse of a Matrix
- Product Integration for the Generalized Abel Equation
