Weighted Radon transforms for which the Chang approximate inversion formula is precise
Roman Novikov (CMAP)
TL;DR
This paper characterizes all weighted Radon transforms on the plane where the Chang approximate inversion formula is exact, and explores related inversion methods like Cormack type inversion.
Contribution
It provides a complete description of weighted Radon transforms with precise Chang inversion, advancing understanding of exact inversion formulas.
Findings
Identifies all weighted Radon transforms with exact Chang inversion
Derives Cormack type inversion formulas for these transforms
Enhances the theoretical framework of Radon transform inversion
Abstract
We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Medical Imaging Techniques and Applications · Image and Object Detection Techniques