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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 computed tomography (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 limited-angle and regionof-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.
This article provides a mathematical classification of artifacts from arbitrary incom-plete X-ray tomography data when using the classical filtered backprojection algorithm. Usingmicrolocal analysis, we prove that all artifacts arise from points at the boundary of the data set.Our results show that, depending on the geometry of the data set boundary, two types of artifactscan arise: object-dependent and object-independent artifacts. The object-dependent artifacts aregenerated by singularities of the object being scanned and these artifacts can extend all along lines.This is a generalization of the streak artifacts observed in limited angle CT. The article also char-acterizes two new phenomena: the object-independent artifacts are caused only by the geometryof the data set boundary; they occur along lines if the boundary of the data set is not smooth andalong curves if the boundary of the data set is smooth. In addition to the geometric descriptionof artifacts, the article also provides characterizations of their strength in Sobolev scale in certaincases. Moreover, numerical reconstructions from simulated and real data are presented illustratingour theorems.This work is motivated by a reconstruction we present from a synchrotron data set in whichartifacts along lines appeared that were independent of the object.The results of this article apply to a wide range of well-known incomplete data problems, in-cluding limited angle CT and region of interest tomography, as well as to unconventional x-ray CTimaging setups. Some of those problems are explicitly addressed in this article, theoretically and numerically.
Reduction of variable-truncation artifacts from beam occlusion during in situ x-ray tomography
(2017)
Many in situ x-ray tomography studies require experimental rigs which may partially occlude the beam and cause parts of the projection data to be missing. In a study of fluid flow in porous chalk using a percolation cell with four metal bars drastic streak artifacts arise in the filtered backprojection (FBP) reconstruction at certain orientations. Projections with non-trivial variable truncation caused by the metal bars are the source of these variable-truncation artifacts. To understand the artifacts a mathematical model of variable-truncation data as a function of metal bar radius and distance to sample is derived and verified numerically and with experimental data. The model accurately describes the arising variable-truncation artifacts across simulated variations of the experimental setup. Three variable-truncation artifact-reduction methods are proposed, all aimed at addressing sinogram discontinuities that are shown to be the source of the streaks. The 'reduction to limited angle' (RLA) method simply keeps only non-truncated projections; the 'detector-directed smoothing' (DDS) method smooths the discontinuities; while the 'reflexive boundary condition' (RBC) method enforces a zero derivative at the discontinuities. Experimental results using both simulated and real data show that the proposed methods effectively reduce variable- truncation artifacts. The RBC method is found to provide the best artifact reduction and preservation of image features using both visual and quantitative assessment. The analysis and artifact-reduction methods are designed in context of FBP reconstruction motivated by computational efficiency practical for large, real synchrotron data. While a specific variable- truncation case is considered, the proposed methods can be applied to general data cut-offs arising in different in situ x-ray tomography experiments.
We study samples with full and partial occlusion causing streak artifacts, and propose two mod-ifications of filtered backprojection for artifact removal. Data is obtained by the SPring-8 synchrotron using a monochromatic parallel-beam scan [1]. Thresholding in the sinogram segments the metal, resulting in edges on which we apply 1) a smooth transition, or 2) a Dirichlet boundary condition.