title: A pointwise limit theorem for filtered backprojection in computed tomography.
abstract: Computed tomography (CT) is one of the most important areas in the modern science and technology. The most popular approach for image reconstruction is filtered backprojection. It is essential to understand the limit behavior of the filtered backprojection algorithms. The classic results on the limit of image reconstruction are typically done in the norm sense. In this paper, we use the method of limited bandwidth to handle filtered backprojection-based image reconstruction when the spectrum of an underlying image is not absolutely integrable. Our main contribution is, assuming the method of limited bandwidth, to prove a pointwise limit theorem for a class of functions practically relevant and quite general. Further work is underway to extend the theory and explore its practical applications.
authors.affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, USA. yangbo-ye@uiowa.edu
authors.forename: Yangbo
authors.initials: Y
authors.lastname: Ye
authors.forename: Jiehua
authors.initials: J
authors.lastname: Zhu
authors.forename: Ge
authors.initials: G
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D014057:Tomography, X-Ray Computed / Q000379:methods*