Isometry property and inversion of a spherical mean Radon transform with centers on a hyperplane
Source abstract
Abstract
The spherical mean Radon transform maps a suitable function f to the integral of f over a sphere. This transform is used in photoacoustic tomography based on the wave equation. There have been studies on the spherical mean Radon transform, including a method that uses an isometry property. In this paper, we demonstrate that the spherical mean Radon transform can be expressed as a convolution with specific (generalized) functions. Additionally, we provide an inversion formula for the spherical mean Radon transform, which is derived from the isometry property of the spherical mean Radon transform.
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Research context
OpenAlex topics: Photoacoustic and Ultrasonic Imaging · Thermography and Photoacoustic Techniques · Optical Imaging and Spectroscopy Techniques
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Affiliations
Department of Mathematics, College of Natural Science, Kyungpook National University , Daegu 41566, Republic of Korea
Funding
National Research Foundation of Korea
References (19)
Show source-provided references
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