Generalized and attenuated radon transforms: restorative approach to the numerical inversion

Kunyansky, Leonid

doi:10.1088/0266-5611/8/5/008

Cited by 35 publications

(44 citation statements)

References 7 publications

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“…These values are in good agreement with that reported by other investtigators [16,19,20] activity concentration D a has been calculated using D a = i/(kt a ): k is attenuation factor [21] from radon-222 transport through the polyethylene (PE) insulating foil [22],  is the calibration coefficient of the radon-222 measuring device in terms of alphatracks cm −2 ·day −1 per Bq·m 3 of radon-222 and t a is the exposure time in hours. Most of buildings have no air-conditioning conditions and some rooms are ventilated by ventilators or simply by opening doors and windows.…”

Section: Experimental Techniquessupporting

confidence: 90%

Physical Factors Affecting the Interior Radon-Concentrations

Abdalla¹,

Jastaniah²

2013

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Researchers have realized that radon-contaminated air inside buildings is a principal way of human exposure to certain healthy-risks. A model is developed to estimate radon concentrations which consider various parameters: in indoor air radon (radon-222) concentration, air permeability of ground, air pressure difference between outdoor and indoor at ground level, ventilation of building ground and number of air changes per hour due to ventilation. The radon-222 transport into building might dominated by diffusion, pressure driven flow or/and a mixture of both depending on the actual values of the various parameters. So, in several and regular periods of time: January, April, July and October, radon-222 concentrations have been measured in ten rooms of five elementary schools and in five rooms of one high school at Qena city (Upper Egypt). This has been carried out using alpha scintillation counters. We have noticed that in three rooms the value has exceeded 200 Bq·m . The experimental results of the present work have been well fitted with the presented model (calculations) which supports the validity of the presented model. So, to decrease the level of indoor air radon-222 concentrations and to reduce its harmful effects it is recommended to follow the suggestions in the present study and to limit as possible the use of ceramic in the building construction, increase the hours of ventilation and to restrict the use of underground floors in buildings, the underground Metro and garage parking should be carefully (and even mandatory) ventilated.

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Section: Experimental Techniquessupporting

confidence: 90%

Physical Factors Affecting the Interior Radon-Concentrations

Abdalla¹,

Jastaniah²

2013

OJBIPHY

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“…The aforementioned transforms P W arise in various domains of pure and applied mathematics; see [LB73], [TM80], [Q83], [Be84], [MQ85], [Fi86], [BQ87], [Sh92], [Kun92], [BQ93], [B93], [Sh93], [KLM95], [Pa96], [ABK98], [Na01], [N02a], [N02b], [BS04], [Bal09], [Gi10], [BJ11], [PG13], [N14], [I16], [Ng17] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A breakdown of injectivity for weighted ray transforms in multidimensions

Goncharov

Novikov

2019

Arkiv För Matematik

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We consider weighted ray-transforms PW (weighted Radon transforms along straight lines) in R d , d ≥ 2, with strictly positive weights W . We construct an example of such a transform with non-trivial kernel in the space of infinitely smooth compactly supported functions on R d . In addition, the constructed weight W is rotation-invariant continuous and is infinitely smooth almost everywhere on R d × S d−1 . In particular, by this construction we give counterexamples to some well-known injectivity results for weighted ray transforms for the case when the regularity of W is slightly relaxed. We also give examples of continous strictly positive W such that dim ker PW ≥ n in the space of infinitely smooth compactly supported functions on R d for arbitrary n ∈ N ∪ {∞}, where W are infinitely smooth for d = 2 and infinitely smooth almost everywhere for d ≥ 3.

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“…Note that the works [GN16], [Gon17] extend to the case of RW , d ≥ 3, the two-dimensional injectivity and reconstruction results of [Kun92], [Nov11], [Nov14], [GuiNov14].…”

Section: Introductionmentioning

confidence: 99%

An Example of Non-uniqueness for Radon Transforms with Continuous Positive Rotation Invariant Weights

Goncharov

Novikov

2018

J Geom Anal

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We consider weighted Radon transforms RW along hyperplanes in R 3 with strictly positive weights W . We construct an example of such a transform with non-trivial kernel KerRW in the space of infinitely smooth compactly supported functions and with continuous weight. Moreover, in this example the weight W is rotation invariant. In particular, by this result we continue studies of , Markoe, Quinto (1985), Boman (1993) and . We also extend our example to the case of weighted Radon transforms along two-dimensional planes in R d , d ≥ 3.

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Generalized and attenuated radon transforms: restorative approach to the numerical inversion

Cited by 35 publications

References 7 publications

Physical Factors Affecting the Interior Radon-Concentrations

Physical Factors Affecting the Interior Radon-Concentrations

A breakdown of injectivity for weighted ray transforms in multidimensions

An Example of Non-uniqueness for Radon Transforms with Continuous Positive Rotation Invariant Weights

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