title: Graph Laplacian tomography from unknown random projections.
abstract: We introduce a graph Laplacian-based algorithm for the tomographic reconstruction of a planar object from its projections taken at random unknown directions. A Laplace-type operator is constructed on the data set of projections, and the eigenvectors of this operator reveal the projection orientations. The algorithm is shown to successfully reconstruct the Shepp-Logan phantom from its noisy projections. Such a reconstruction algorithm is desirable for the structuring of certain biological proteins using cryo-electron microscopy.
authors.affiliation: Department of Mathematics, Program in Applied Mathematics, Yale University, New Haven, CT 06520-8283, USA. coifman-ronald@yale.edu
authors.forename: Ronald R
authors.initials: RR
authors.lastname: Coifman
authors.forename: Yoel
authors.initials: Y
authors.lastname: Shkolnisky
authors.forename: Fred J
authors.initials: FJ
authors.lastname: Sigworth
authors.forename: Amit
authors.initials: A
authors.lastname: Singer
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D015233:Models, Statistical; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D041622:Tomography, Optical / Q000379:methods*