Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography
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Abstract
The operators of longitudinal and transverse ray transforms acting on vector fields on the unit disc are considered in the paper. The goal is to construct SVD-decompositions of the operators and invert them approximately by means of truncated decomposition for the parallel scheme of data acquisition. The orthogonal bases in the initial spaces and the image spaces are constructed using harmonic, Jacobi and Gegenbauer polynomials. Based on the obtained decompositions inversion formulas are derived and the polynomial approximations for the inverse operators are obtained. Numerical tests for data sets with different noise levels of smooth and discontinuous fields show the validity of the approach for the reconstruction of solenoidal or potential parts of vector fields from their ray transforms.
© de Gruyter 2011
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- Uniqueness theorems from partial information of the potential on a graph
- On the approximations of derivatives of integrated semigroups. II
- Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography
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Articles in the same Issue
- An inverse method for bounded error parameter identification
- An inverse problem for the wave equation
- Shrinkage rules for variational minimization problems and applications to analytical ultracentrifugation
- Reconstruction of initial Tsunami waveforms by a truncated SVD method
- Uniqueness theorems from partial information of the potential on a graph
- On the approximations of derivatives of integrated semigroups. II
- Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography
- Uniqueness in inverse scattering of elastic waves by three-dimensional polyhedral diffraction gratings
- Asymptotic inversion formulas in 3D vector field tomography for different geometries
