Inverting Spherical Radon Transform by a Closed-form Formula: A Microlocal Analytic Point of View

2013/07/09 by Linh V. Nguyen, Nguyen, Linh V.
Computer Science · Engineering · Mathematics · Medicine · #35S30 #53C65 #92C55 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #math.AP #math.CA #msc:35S30 #msc:53C65 #msc:92C55

paper · pdf · doi:10.48550/arxiv.1307.2634

openalex publication_date 2013/07/09 · arxiv created 2013/07/10 · arxiv updated 2013/07/11 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Let \mR be the restriction of the spherical Radon transform to the set of spheres centered on a hypersurface \mS. We study the inversion of \mR by a closed-form formula. We approach the problem by studying an oscillatory integral, which depends on the observation surface \mS as a parameter. We then derive various microlocal analytic properties of the associated closed-form inversion formula.

Citations

• Inverting the spherical Radon transform for physically meaningful functions

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