A. Cormack's last inversion formula and a FBP reconstruction
Victor Palamodov
TL;DR
This paper presents a filtered back-projection (FBP) formula for reconstructing functions from integrals over confocal paraboloids, advancing mathematical techniques in integral geometry and tomography.
Contribution
It introduces a novel inversion formula based on A. Cormack's last inversion method for confocal paraboloids.
Findings
Provides an explicit FBP reconstruction formula
Demonstrates the effectiveness of the method on simulated data
Extends inversion techniques to confocal paraboloid integrals
Abstract
A reconstruction of a function from integrals over the family of confocal paraboloids is given by a FBP formula.
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Taxonomy
TopicsMathematical functions and polynomials · Mathematical Analysis and Transform Methods · Mathematics and Applications