Isometry property and inversion of the Radon transform over a family of paraboloids

Jeongmin Kim, Sunghwan Moon

Research output: Contribution to journalArticlepeer-review

Abstract

Integral geometry problems involve finding a desired function from its integrals on a surface. These problems are closely intertwined with the generalized Radon transform, and obtaining an inversion formula for it is pivotal in solving integral geometry problems. The applications of integral geometry span various fields, including tomography, radar, and radiology. Particularly noteworthy is the recovery of a function from integrals over a parabola, which holds significance in reflection seismology. In our study, we concentrate on the transform that maps a real-valued smooth function with compact support to integrals over the paraboloid. This transform, along with its dual, can be expressed as convolutions of kernels and given functions, and we have derived inversion formulas based on their isometric properties.

Original languageEnglish
Pages (from-to)8047-8052
Number of pages6
JournalFilomat
Volume38
Issue number23
DOIs
StatePublished - 2024

Keywords

  • Inversion formula
  • Paraboloid
  • Radon transform
  • tomography

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