Modified Radon transform inversion using moments
-
Hayoung Choi
and
Robert Mnatsakanov
Abstract
Moment methods to reconstruct images from their Radon transforms are both natural and useful. They can be used to suppress noise or other spurious effects and can lead to highly efficient reconstructions from relatively few projections. We establish a modified Radon transform (MRT) via convolution with a mollifier and obtain its inversion formula. The relationship of the moments of the Radon transform and the moments of its modified Radon transform is derived, and MRT data is used to provide a uniform approximation to the original density function. The reconstruction algorithm is implemented, and a simple density function is reconstructed from moments of its modified Radon transform. Numerical convergence of this reconstruction is shown to agree with the derived theoretical results.
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Articles in the same Issue
- Frontmatter
- Modified Radon transform inversion using moments
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- Two closed novel formulas for the generalized inverse A T,S (2) of a complex matrix with given rank
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- Isospectral sets for transmission eigenvalue problem
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- Joint inversion of compact operators
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Articles in the same Issue
- Frontmatter
- Modified Radon transform inversion using moments
- Inverse source problem for a distributed-order time fractional diffusion equation
- Two closed novel formulas for the generalized inverse A T,S (2) of a complex matrix with given rank
- The problem of determining the one-dimensional kernel of viscoelasticity equation with a source of explosive type
- Inverse problems for a class of linear Sobolev type equations with overdetermination on the kernel of operator at the derivative
- Isospectral sets for transmission eigenvalue problem
- Stability estimate for an inverse problem of the convection-diffusion equation
- The enclosure method for the heat equation using time-reversal invariance for a wave equation
- Joint inversion of compact operators
- Inverse problem of breaking line identification by shape optimization
- The backward problem of parabolic equations with the measurements on a discrete set
- Optimal convergence rates for inexact Newton regularization with CG as inner iteration
