Full Characterization of Reconstruction Artifacts from Arbitrary Incomplete X-ray CT Data
Year: 2017
Type: preprint
Abstract: This article provides a mathematical classification of artifacts from arbitrary incomplete X-ray tomography data when using the classical filtered backprojection algorithm. Using microlocal 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 artifacts can arise object-dependent and object-independent artifacts. The object-dependent artifacts are generated 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 characterizes two new phenomena: the object-independent artifacts are caused only by the geometry of the data set boundary; they occur along lines if the boundary of the data set is not smooth and along curves if the boundary of the data set is smooth. In addition to the geometric description of artifacts, the article also provides characterizations of their strength in Sobolev scale in certain cases. Moreover, numerical reconstructions from simulated and real data are presented illustrating our theorems.
This work is motivated by a reconstruction we present from a synchrotron data set in which artifacts 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, including limited angle CT and region of interest tomography, as well as to unconventional x-ray CT imaging setups. Some of those problems are explicitly addressed in this article, theoretically and numerically.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2783631258