[Paper Review] Full Characterization of Reconstruction Artifacts from Arbitrary Incomplete X-ray CT Data

Leise Borg, Jürgen Frikel+2 more|arXiv (Cornell University)|Jul 4, 2017

Medical Imaging Techniques and Applications47 references3 citations

TL;DR

This paper provides a mathematical classification of reconstruction artifacts in incomplete X-ray CT using microlocal analysis, showing that artifacts arise from the boundary of the data set. It identifies two types: object-dependent artifacts extending along lines due to object singularities, and object-independent artifacts along lines (non-smooth boundary) or curves (smooth boundary), with strength characterized in Sobolev spaces.

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.

Motivation & Objective

• To mathematically classify reconstruction artifacts in incomplete X-ray CT data when using filtered backprojection.
• To determine the origin of artifacts by analyzing the geometry of the data set boundary.
• To distinguish between object-dependent artifacts (caused by object singularities) and object-independent artifacts (caused solely by data boundary geometry).
• To characterize the strength of artifacts in Sobolev spaces for specific cases.
• To validate theoretical findings with numerical reconstructions from simulated and real synchrotron data.

Proposed method

• Employing microlocal analysis to study the singularities in the reconstructed image arising from incomplete X-ray data.
• Analyzing the propagation of singularities through the filtered backprojection algorithm to trace artifact origins to the boundary of the data set.
• Classifying artifacts based on the smoothness and geometry of the data set boundary: non-smooth boundaries produce line-like artifacts, smooth boundaries produce curve-like artifacts.
• Deriving Sobolev-scale characterizations of artifact strength under specific geometric and analytic conditions.
• Validating theoretical predictions with numerical reconstructions from both simulated and real synchrotron X-ray CT data.
• Using a reconstruction from a real synchrotron data set as a motivating example for the emergence of object-independent line artifacts.

Experimental results

Research questions

• RQ1 What determines the origin of artifacts in filtered backprojection reconstructions from incomplete X-ray CT data?
• RQ2 How do the geometry and smoothness of the data set boundary influence the shape and structure of artifacts?
• RQ3 What distinguishes object-dependent artifacts from object-independent artifacts in terms of their formation and spatial distribution?
• RQ4 Can the strength of artifacts be quantified in Sobolev spaces, and under what conditions?
• RQ5 To what extent do the theoretical predictions match numerical reconstructions from real and simulated data?

Key findings

• All artifacts in filtered backprojection reconstructions from incomplete X-ray data originate from the boundary of the data set.
• Object-dependent artifacts arise from singularities in the scanned object and extend along straight lines, generalizing the streak artifacts seen in limited angle CT.
• Object-independent artifacts are caused solely by the geometry of the data set boundary: they appear along lines if the boundary is non-smooth and along curves if the boundary is smooth.
• The strength of artifacts can be characterized in Sobolev spaces under certain geometric and analytic conditions, providing a quantitative measure of artifact intensity.
• Numerical reconstructions from both simulated and real synchrotron data confirm the theoretical predictions, including the presence of object-independent line artifacts.