Quantitative Analysis of Metal Artifacts in X-ray Tomography

Palacios, Benjamin; Uhlmann, Günther

doi:10.1137/17m1160392

Cited by 8 publications

(12 citation statements)

References 13 publications

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“…For metal artifacts, there is vast literature (see, e.g., [3]) for artifact reduction methods, and we believe that those methods might also be useful for certain other incomplete data tomography problems. In [39,43,51], the authors have effectively used microlocal analysis to understand these related problems. Our theory is developed based on the continuous case -we view the data as functions on S 1 × R, not just defined at discrete points.…”

Section: 1mentioning

confidence: 99%

“…This can be dealt with as an incomplete data problem by excluding data over lines through the metal. Recently, this problem has been mathematically modeled in a sophisticated way using microlocal analysis in [39,43,51]. A related problem is studied in [8,38,41], where the authors develop a streak reduction method for quantitative susceptibility mapping.…”

Section: Introductionmentioning

confidence: 99%

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Analyzing Reconstruction Artifacts from Arbitrary Incomplete X-ray CT Data

Borg

Frikel²,

Jørgensen

et al. 2018

SIAM J. Imaging Sci.

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This article provides a mathematical analysis of singular (nonsmooth) artifacts added to reconstructions by filtered backprojection (FBP) type algorithms for X-ray CT with arbitrary incomplete data. We prove that these singular artifacts arise from points at the boundary of the data set. Our results show that, depending on the geometry of this boundary, two types of artifacts can arise: object-dependent and object-independent artifacts. Object-dependent artifacts are generated by singularities of the object being scanned and these artifacts can extend along lines. They generalize the streak artifacts observed in limited-angle tomography. Object-independent artifacts, on the other hand, are essentially independent of the object and take one of two forms: streaks on lines if the boundary of the data set is not smooth at a point and curved artifacts if the boundary is smooth locally. We prove that these streak and curve artifacts are the only singular artifacts that can occur for FBP in the continuous case. In addition to the geometric description of artifacts, the article provides characterizations of their strength in Sobolev scale in certain cases. The results of this article apply to the well-known incomplete data problems, including limitedangle and region-of-interest tomography, as well as to unconventional X-ray CT imaging setups that arise in new practical applications. Reconstructions from simulated and real data are analyzed to illustrate our theorems, including the reconstruction that motivated this work-a synchrotron data set in which artifacts appear on lines that have no relation to the object.

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Section: 1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analyzing Reconstruction Artifacts from Arbitrary Incomplete X-ray CT Data

Borg

Frikel²,

Jørgensen

et al. 2018

SIAM J. Imaging Sci.

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show abstract

“…All the two-dimensional singularities spanned by those at tangent points do not necessarily propagate, but the singularities of only two normal directions at the tangent points spread in the whole (n − 2)-dimensional plane. Our method of analysis of the streaking artifacts is based on the idea of [15], and the results are some generalization of recent results of [16] and [15] for the X-ray transform on the two-dimensional plane. The case that D is a disjoint union of finite numbers of convex polygons in R 2 was also studied in [16] and [15].…”

Section: Figurementioning

confidence: 98%

“…Moreover the canonical relation of R n−1 is well-known and applied to the microlocal analysis of CT images for n = 2. See [1], [13], [15], [16], [17] and [18]. As far as the author knows the canonical relation of R d for d =n − 1 was rarely considered so far.…”

Section: Introductionmentioning

confidence: 99%

“…Their results show the qualitative properties of the metal streaking artifacts. Moreover in [15] Palacios, Uhlmann and Wang developed the results of [16]. By using the notion of paired Lagrangian distributions introduced in [4], they proved that the metal streaking artifacts are conormal distributions supported on all the common tangential lines.…”

Section: Introductionmentioning

confidence: 99%

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Microlocal analysis of d-plane transform on the Euclidean space

Chihara¹

2021

Preprint

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We study the basic properties of d-plane transform on the Euclidean space as a Fourier integral operator, and its application to the microlocal analysis of streaking artifacts in its filtered backprojection. The d-plane transform is defined by integrals of functions on the n-dimensional Euclidean space over all the d-dimensional planes, where 0 < d < n. This maps functions on the Euclidean space to those on the affine Grassmannian G(d, n). This is said to be X-ray transform if d = 1 and Radon transform if d = n − 1. When n = 2 the X-ray transform is thought to be measurements of CT scanners. In this paper we obtain concrete expression of the canonical relation of the d-plane transform and quantitative properties of the filtered back-projection of the product of the images of the d-plane transform. The latter one is related to the metal streaking artifacts of CT images, and some generalization of recent results of Park-Choi-Seo (2017) and Palacios-Uhlmann-Wang (2018) for the X-ray transform on the plane.

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Bargmann Transform on the Space of Hyperplanes

Chihara

2022

J Fourier Anal Appl

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Quantitative Analysis of Metal Artifacts in X-ray Tomography

Cited by 8 publications

References 13 publications

Analyzing Reconstruction Artifacts from Arbitrary Incomplete X-ray CT Data

Analyzing Reconstruction Artifacts from Arbitrary Incomplete X-ray CT Data

Microlocal analysis of d-plane transform on the Euclidean space

Bargmann Transform on the Space of Hyperplanes

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