Plancherel formula for the attenuated Radon transform
Enik\H{o} Dinny\'es, Tibor \'Odor
TL;DR
This paper establishes a Plancherel formula for the attenuated Radon transform, extending the mathematical understanding of this transform with potential applications in stereology and imaging.
Contribution
It introduces a Plancherel-type formula for the attenuated Radon transform based on Novikov's inversion formula, advancing the theoretical framework of integral transforms.
Findings
Proves a Plancherel formula for the attenuated Radon transform
Extends the mathematical theory of the Radon transform with attenuation
Provides tools for improved imaging and stereology techniques
Abstract
Motivated by stereology, based on Novikov's inversion formula, we prove a Plancherel-type formula for the attenuated Radon transform.
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Taxonomy
TopicsMedical Imaging Techniques and Applications · Mathematical Analysis and Transform Methods · Numerical methods in inverse problems