The V-line transform with some generalizations and cone differentiation Article Swipe
Gaik Ambartsoumian
,
Mohammad Javad Latifi Jebelli
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1088/1361-6420/aafcf3
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.1088/1361-6420/aafcf3
The paper studies various properties of the V-line transform (VLT) in the plane and conical Radon transform (CRT) in $\mathbb{R}^n$. 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 VLT and CRT, as well as proving some previously known results using more intuitive geometric ideas. Using our inversion formula for 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 Cone Differentiation Theorem.
Related Topics
Concepts
Line integral
Conical surface
Inversion (geology)
Mathematics
Radon transform
Generalization
Transformation (genetics)
Pure mathematics
Cone (formal languages)
Line (geometry)
Line segment
Mathematical analysis
Geometry
Algorithm
Integral equation
Gene
Chemistry
Structural basin
Biochemistry
Paleontology
Biology
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.1088/1361-6420/aafcf3
- OA Status
- green
- References
- 52
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2807316896
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https://doi.org/10.1088/1361-6420/aafcf3Digital Object Identifier
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The V-line transform with some generalizations and cone differentiationWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2019Year of publication
- Publication date
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2019-01-09Full publication date if available
- Authors
-
Gaik Ambartsoumian, Mohammad Javad Latifi JebelliList of authors in order
- Landing page
-
https://doi.org/10.1088/1361-6420/aafcf3Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1612.05113Direct OA link when available
- Concepts
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Line integral, Conical surface, Inversion (geology), Mathematics, Radon transform, Generalization, Transformation (genetics), Pure mathematics, Cone (formal languages), Line (geometry), Line segment, Mathematical analysis, Geometry, Algorithm, Integral equation, Gene, Chemistry, Structural basin, Biochemistry, Paleontology, BiologyTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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52Number of works referenced by this work
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20Other works algorithmically related by OpenAlex
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| referenced_works | https://openalex.org/W1995777500, https://openalex.org/W1988716939, https://openalex.org/W2071414958, https://openalex.org/W2274344128, https://openalex.org/W2146977804, https://openalex.org/W1555941245, https://openalex.org/W2156977738, https://openalex.org/W2008775029, https://openalex.org/W2066730497, https://openalex.org/W2963409756, https://openalex.org/W4213327626, https://openalex.org/W2072450612, https://openalex.org/W2022879507, https://openalex.org/W2589026729, https://openalex.org/W50621378, https://openalex.org/W4245937453, https://openalex.org/W2039538584, https://openalex.org/W2316227792, https://openalex.org/W2050255344, https://openalex.org/W1646332070, https://openalex.org/W2328806788, https://openalex.org/W2231835938, https://openalex.org/W2534899473, https://openalex.org/W2586432563, https://openalex.org/W1999934946, https://openalex.org/W1734053220, https://openalex.org/W2163413008, https://openalex.org/W1999834333, https://openalex.org/W2405129139, https://openalex.org/W2605716036, https://openalex.org/W2963048996, https://openalex.org/W2155914286, https://openalex.org/W2134562742, https://openalex.org/W2750405289, https://openalex.org/W2963842126, https://openalex.org/W2962841134, https://openalex.org/W2792800705, https://openalex.org/W3115258393, https://openalex.org/W2290715407, https://openalex.org/W2050976450, https://openalex.org/W2085443106, https://openalex.org/W2490929499, https://openalex.org/W227597898, https://openalex.org/W2068445652, https://openalex.org/W2543813466, https://openalex.org/W2230117435, https://openalex.org/W3103782609, https://openalex.org/W39337161, https://openalex.org/W3101023559, https://openalex.org/W3100434883, https://openalex.org/W2087319496, https://openalex.org/W3106532617 |
| referenced_works_count | 52 |
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| abstract_inverted_index.ideas. | 102 |
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| abstract_inverted_index.point. | 40 |
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| abstract_inverted_index.Compton | 74 |
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| abstract_inverted_index.article, | 152 |
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| abstract_inverted_index.transformation | 115 |
| abstract_inverted_index.$\mathbb{R}^n$. | 19 |
| abstract_inverted_index.Differentiation | 167 |
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