Investigation of scattering and absorbing media by the methods of X-ray tomography

Аниконов, Д. С.; Прохоров, И. В.; Kovtanyuk, Andrey E.

doi:10.1515/jiip.1993.1.4.259

Cited by 34 publications

(53 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The forward problem (1), (2) and (3) admits a unique solution under natural assumptions on μ, μ a and η [41]. The homogeneous condition g − (x, θ ,t) = 0 specifies that no photons travel in an inward direction at the boundary, except for source terms [25, p. R50], which is the case for BLT.…”

Section: Formulation Of Bltmentioning

confidence: 99%

Image reconstruction for bioluminescence tomography from partial measurement

Zhou

Cheng

et al. 2007

Opt. Express

View full text Add to dashboard Cite

Abstract:The bioluminescence tomography is a novel molecular imaging technology for small animal studies. Known reconstruction methods require the completely measured data on the external surface, although only partially measured data is available in practice. In this work, we formulate a mathematical model for BLT from partial data and generalize our previous results on the solution uniqueness to the partial data case. Then we extend two of our reconstruction methods for BLT to this case. The first method is a variant of the well-known EM algorithm. The second one is based on the Landweber scheme. Both methods allow the incorporation of knowledgebased constraints. Two practical constraints, the source non-negativity and support constraints, are introduced to regularize the BLT problem and produce stability. The initial choice of both methods and its influence on the regularization and stability are also discussed. The proposed algorithms are evaluated and validated with intensive numerical simulation and a physical phantom experiment. Quantitative results including the location and source power accuracy are reported. Various algorithmic issues are investigated, especially how to avoid the inverse crime in numerical simulations.

show abstract

Section: Formulation Of Bltmentioning

confidence: 99%

Image reconstruction for bioluminescence tomography from partial measurement

Zhou

Cheng

et al. 2007

Opt. Express

View full text Add to dashboard Cite

show abstract

“…For example, it may be used for (η,ω) G Γ" 1 ". We assume that radiation sources are essential J 2 (r,cj) + Ιι\(τ,ω) > 0, (r,cj) G GO x Ω, which provides positiveness of the function /(r,ω) for those (r,cj) that satisfy formula (1.4) [1].…”

Section: S Anikonovmentioning

confidence: 99%

“…

This paper summarizes recent author's works [1][2][3][4]. The tomography problem is setted, formulated in the terms of radiation transfer.

…”

mentioning

confidence: 94%

See 1 more Smart Citation

Integro-differential indicator of nonhomogeneity in tomography problem

Аниконов¹

1999

Jiip

Self Cite

View full text Add to dashboard Cite

This paper summarizes recent author's works [1][2][3][4]. The tomography problem is setted, formulated in the terms of radiation transfer. The uniqueness theorem is established for this problem.In this paper we introduce new notions: the nonhomogeneity indicator, the visibility measure, the visibility condition. The algorithm of determination of internal medium structure is constructed, and its testing is done.

show abstract

“…Then the main results of the electromagnetic cloaking theory were expanded to an acoustic cloaking [6] and to cloaking static (magnetic, electric and thermal) fields (see, e.g., [7,8,9]). Papers [10,11] are devoted to studying invisibility problems in X-ray tomography.…”

Section: Introductionmentioning

confidence: 99%

Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method

Алексеев

Tokhtina

Соболева

2017

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Abstract. Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields -electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.

show abstract

Investigation of scattering and absorbing media by the methods of X-ray tomography

Cited by 34 publications

References 0 publications

Image reconstruction for bioluminescence tomography from partial measurement

Image reconstruction for bioluminescence tomography from partial measurement

Integro-differential indicator of nonhomogeneity in tomography problem

Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method

Contact Info

Product

Resources

About