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This short paper closely follows the presentation on Monday May 27, 2024 at the 2024 IPMS Conference (Malta), in session M1. The title was “A Medley of Range Conditions for Divergent-Beam Transforms”. To set the scene, the well-known polynomial moment conditions are recalled, for the x-ray transform in two-dimensions. The “projection form” of these conditions is noted. Then three divergent-beam geometries are presented: fanbeam projections with sources along a line; cone-beam projections with source on a circle; and truncated fanbeam projections along a circle. Links to the polynomial moment conditions are pointed out.

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Range Conditions for Some Divergent-Beam Transforms

  • 会议论文

  • 发表日期：

    2025年

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  • Rolf Clackdoyle

摘要

This short paper closely follows the presentation on Monday May 27, 2024 at the 2024 IPMS Conference (Malta), in session M1. The title was “A Medley of Range Conditions for Divergent-Beam Transforms”. To set the scene, the well-known polynomial moment conditions are recalled, for the x-ray transform in two-dimensions. The “projection form” of these conditions is noted. Then three divergent-beam geometries are presented: fanbeam projections with sources along a line; cone-beam projections with source on a circle; and truncated fanbeam projections along a circle. Links to the polynomial moment conditions are pointed out.