Abstract
We present in this work alternative analytic formulations for the fan-beam tomographic backprojection operation and its associated adjoint transform in standard (equiangular) and linear (equidistant) detector geometries.
The proposed formulations are obtained from a recent backprojection theorem in parallel tomography.
Such formulations are written as a Bessel–Neumann series in the frequency domain that can be implemented as an
Funding source: Fonds Wetenschappelijk Onderzoek
Award Identifier / Grant number: S004217N
Funding statement: PG was supported by the FWO-SBO MetroFleX project (grant agreement S004217N).
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Variation method solving of the inverse problems for Schrödinger-type equation
- Stability estimate for scalar image velocimetry
- Inverse problems for equations of a mixed parabolic-hyperbolic type with power degeneration in finding the right-hand parts that depend on time
- Inverse problem for integro-differential Kelvin–Voigt equations
- A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces
- Tensor tomography of the residual stress field in graded-index YAG’s single crystals
- Uniqueness and stability for inverse source problem for fractional diffusion-wave equations
- Reconstruction of modified transmission eigenvalues using Cauchy data
- Alternative fan-beam backprojection and adjoint operators
- The problem of determining multiple coefficients in an ultrahyperbolic equation
- A note on the degree of ill-posedness for mixed differentiation on the d-dimensional unit cube
- A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform
Articles in the same Issue
- Frontmatter
- Variation method solving of the inverse problems for Schrödinger-type equation
- Stability estimate for scalar image velocimetry
- Inverse problems for equations of a mixed parabolic-hyperbolic type with power degeneration in finding the right-hand parts that depend on time
- Inverse problem for integro-differential Kelvin–Voigt equations
- A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces
- Tensor tomography of the residual stress field in graded-index YAG’s single crystals
- Uniqueness and stability for inverse source problem for fractional diffusion-wave equations
- Reconstruction of modified transmission eigenvalues using Cauchy data
- Alternative fan-beam backprojection and adjoint operators
- The problem of determining multiple coefficients in an ultrahyperbolic equation
- A note on the degree of ill-posedness for mixed differentiation on the d-dimensional unit cube
- A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform