title: A differentiable Shepp-Logan phantom and its applications in exact cone-beam CT.
abstract: Recently, several exact cone-beam reconstruction algorithms, such as the generalized filtered-backprojection (FBP) and backprojection-filtration (BPF) methods, have been developed to solve the long object problem. Although the well-known 3D Shepp-Logan phantom (SLP) is often used to validate these algorithms, it is deficient due to the discontinuity of the SLP. In this paper, we first construct a differentiable polynomial function to approximate the unit rectangular function on [-1, 1]. Then, we use this function to obtain a differentiable ellipsoid phantom, whose x-ray transform is differentiable for any smooth scanning trajectory. Finally, we propose a differentiable Shepp-Logan phantom (DSLP) for numerical simulation of the exact cone-beam CT algorithms. Our numerical simulation shows that the reconstructed DSLP has a better image quality than the reconstructed SLP, and is complementary to the traditional SLP for evaluation of the exact cone-beam CT algorithms.
authors.affiliation: CT/Micro-CT Laboratory, Department of Radiology, University of Iowa, Iowa City, 52242, USA. hengyong-yu@uiowa.edu
authors.forename: Hengyong
authors.initials: H
authors.lastname: Yu
authors.forename: Shiying
authors.initials: S
authors.lastname: Zhao
authors.forename: Ge
authors.initials: G
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D007091:Image Processing, Computer-Assisted; D021621:Imaging, Three-Dimensional; D015233:Models, Statistical; D019047:Phantoms, Imaging; D011857:Radiographic Image Interpretation, Computer-Assisted; D012984:Software; D036542:Tomography, Spiral Computed / Q000379:methods; D014057:Tomography, X-Ray Computed / Q000379:methods*; D014965:X-Rays