Inversion formulas for quarter-spherical Radon transforms

Gyeongha Hwang; Sunghwan Moon; Gyeongha Hwang; Sunghwan Moon

doi:10.3934/math.20231600

AIMS Mathematics

2023, Volume 8, Issue 12: 31258-31267. doi: 10.3934/math.20231600

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Inversion formulas for quarter-spherical Radon transforms

Gyeongha Hwang ¹,
Sunghwan Moon ^{2
,
,}

1.
Department of Mathematics, Yeungnam University, Gyeongsan 38541, Republic of Korea
2.
Department of Mathematics, Kyungpook National University, Daegu 41566, Republic of Korea

Received: 06 June 2023 Revised: 08 November 2023 Accepted: 15 November 2023 Published: 24 November 2023
MSC : 35L05, 44A12

The applications of spherical Radon transforms include synthetic aperture radar, sonar tomography, and medical imaging modalities. A spherical Radon transform maps a function to its integrals over a family of spheres. Recently, several types of incomplete spherical Radon transforms have received attention in research. This study examines two types of quarter-spherical Radon transforms that assign a function to its integral over a quarter of a sphere: 1) center of a quarter sphere of integration on a plane, and 2) center on a line and the rotation of the quarter sphere. Furthermore, we present inversion formulas for these two quarter-spherical Radon transforms.
- photoacoutic,
- tomography,
- Radon transform,
- inversion,
- a quarter sphere
Citation: Gyeongha Hwang, Sunghwan Moon. Inversion formulas for quarter-spherical Radon transforms[J]. AIMS Mathematics, 2023, 8(12): 31258-31267. doi: 10.3934/math.20231600

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Abstract

The applications of spherical Radon transforms include synthetic aperture radar, sonar tomography, and medical imaging modalities. A spherical Radon transform maps a function to its integrals over a family of spheres. Recently, several types of incomplete spherical Radon transforms have received attention in research. This study examines two types of quarter-spherical Radon transforms that assign a function to its integral over a quarter of a sphere: 1) center of a quarter sphere of integration on a plane, and 2) center on a line and the rotation of the quarter sphere. Furthermore, we present inversion formulas for these two quarter-spherical Radon transforms.

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