Operator identities relating sonar and Radon transforms in Euclidean space

2006/07/18 by Aleksei Beltukov, David Feldman, Beltukov, Aleksei +1
Engineering · Mathematics · Physics and Astronomy · #44A12 #Advanced Differential Geometry Research #Advanced SAR Imaging Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Inertial Sensor and Navigation #math.CA #math.FA #msc:44A12

paper · pdf · doi:10.48550/arxiv.math/0607437

20 pages, 3 figures

arxiv created 2006/07/18 · openalex publication_date 2006/07/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish new relations which connect Euclidean sonar transforms (integrals taken over spheres with centers in a hyperplane) with classical Radon transforms. The relations, stated as operator identities, allow us to reduce the inversion of sonar transforms to classical Radon inversion.

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