Graph Laplacian tomography from unknown random projections.
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.
Coifman
Ronald R
RR
Department of Mathematics, Program in Applied Mathematics, Yale University, New Haven, CT 06520-8283, USA. coifman-ronald@yale.edu
Shkolnisky
Yoel
Y
Sigworth
Fred J
FJ
Singer
Amit
A
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*