A motion artefact study and locally deforming objects in computerized tomography

Hahn, Bernadette N.

doi:10.1088/1361-6420/aa8d7b

Cited by 6 publications

(4 citation statements)

References 23 publications

(63 reference statements)

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“…The proposed approach has the advantage of avoiding an expensive precomputation step of the reconstruction kernels. In particular, we extend our previous results on dynamic CT from [18], and also [16,17], to this more general class of dynamic imaging operators by using methods from microlocal analysis.…”

Section: Introductionsupporting

confidence: 56%

An efficient reconstruction approach for a class of dynamic imaging operators

Hahn

Garrido

2019

Inverse Problems

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This article deals with the problem of recovering an image from tomographic data corrupted by the motion of an object. Using generalized Radon transforms as modeling for the dynamic imaging operators, we present a novel approach for the reconstruction process. The proposed method, motivated by results on microlocal analysis, approximates the solution via a filtered backprojection-type algorithm which has the advantage of being quick to implement. The numerical results applied on dynamic photoacoustic tomography (PAT) data corroborate the efficiency and relevance of the proposed method.

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Section: Introductionsupporting

confidence: 56%

An efficient reconstruction approach for a class of dynamic imaging operators

Hahn

Garrido

2019

Inverse Problems

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“…Many time-dependent problems have been addressed and studied in relation to applications (see [27]), for instance, in dynamic computerized tomography [14,15], magnetic resonance imaging [17], emission tomography [18], magnetic particle imaging [1,3,26,31], or structural health monitoring [30,32]. We state some recent examples for dynamic inverse problems in real-world applications in the following:…”

Section: Introductionmentioning

confidence: 99%

Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces

Burger,

Schuster,

Wald

2024

Inverse Problems

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We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover parameters from given observations where the parameters or the data depend on time. There are various important applications being subject of current research that belong to this class of problems. Typically inverse problems are ill-posed in the sense that already small noise in the data causes tremendous errors in the solution. In this article we present two diﬀerent concepts of ill-posedness: temporally (pointwise) ill-posedness and uniform ill-posedness with respect to the Lebesgue-Bochner setting. We investigate the two concepts by means of a typical setting consisting of a time-depending observation operator composed by a compact operator. Furthermore we develop regularization methods that are adapted to the respective class of ill-posedness.

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“…Motion compensation strategies are also investigated in [3,11,13]. In [12] the relation between motion and resolution has been investigated.…”

Section: Introductionmentioning

confidence: 99%

Well-defined forward operators in dynamic diffractive tensor tomography using viscosity solutions of transport equations

Lukas¹,

Schuster²

2021

Preprint

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We consider a general setting for dynamic tensor field tomography in an inhomogeneous refracting and absorbing medium as inverse source problem for the associated transport equation. Following Fermat's principle the Riemannian metric in the considered domain is generated by the refractive index of the medium. There is wealth of results for the inverse problem of recovering a tensor field from its longitudinal ray transform in a static euclidean setting, whereas there are only few inversion formulas and algorithms existing for general Riemannian metrics and time-dependent tensor fields. It is a well-known fact that tensor field tomography is equivalent to an inverse source problem for a transport equation where the ray transform serves as given boundary data. We prove that this result extends to the dynamic case. Interpreting dynamic tensor tomography as inverse source problem represents a holistic approach in this field. To guarantee that the forward mappings are well-defined, it is necessary to prove existence and uniqueness for the underlying transport equations. Unfortunately, the bilinear forms of the associated weak formulations do not satisfy the coercivity condition. To this end we transfer to viscosity solutions and prove their unique existence in appropriate Sobolev (static case) and Sobolev-Bochner (dynamic case) spaces under a certain assumption that allows only small variations of the refractive index. Numerical evidence is given that the viscosity solution solves the original transport equation if the viscosity term turns to zero.Keywords attenuated refractive dynamic ray transform of tensor fields • geodesics • transport equation • viscosity solutions TFT has many possible applications. One is the reconstruction of velocity fields of liquids and gases. This can be used, e.g., to represent blood flows in medicine. TFT is also used in electron tomography, industry, geo-and astrophysics to name only a few application fields. Pioneered by Norton [20] in 1988, fundamental results on Doppler tomography

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A motion artefact study and locally deforming objects in computerized tomography

Cited by 6 publications

References 23 publications

An efficient reconstruction approach for a class of dynamic imaging operators

An efficient reconstruction approach for a class of dynamic imaging operators

Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces

Well-defined forward operators in dynamic diffractive tensor tomography using viscosity solutions of transport equations

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