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• W2951404038 abstract "The paper studies various properties of the V-line transform (VLT) in the plane and the conical Radon transform (CRT) in . The VLT maps a function to a family of its integrals along trajectories made of two rays emanating from a common point. The CRT considered in this paper maps a function to a set of its integrals over surfaces of polyhedral cones. These types of operators appear in mathematical models of single scattering optical tomography, Compton camera imaging and other applications. We derive new explicit inversion formulae for the VLT and the CRT, as well as proving some previously known results using more intuitive geometric ideas. Using our inversion formula for the VLT, we describe the range of that transformation when applied to a fairly broad class of functions and prove some support theorems. The efficiency of our method is demonstrated on several numerical examples. As an auxiliary result that plays a big role in this article, we derive a generalization of the fundamental theorem of calculus, which we call the cone differentiation theorem." @default.
• W2951404038 created "2019-06-27" @default.
• W2951404038 creator A5033797478 @default.
• W2951404038 creator A5066199956 @default.
• W2951404038 date "2019-02-04" @default.
• W2951404038 modified "2023-09-25" @default.
• W2951404038 title "The V-line transform with some generalizations and cone differentiation" @default.
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• W2951404038 doi "https://doi.org/10.1088/1361-6420/aafcf3" @default.
• W2951404038 hasPublicationYear "2019" @default.
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