Graph Laplacian Tomography From Unknown Random Projections

Author

Coifman, Ronald R. ; Shkolnisky, Yoel ; Sigworth, Fred J. ; Singer, Amit

Author_Institution

Dept. of Math., Yale Univ., New Haven, CT

Volume

17

Issue

10

fYear

2008

Firstpage

1891

Lastpage

1899

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.

Keywords

Laplace equations; eigenvalues and eigenfunctions; graph theory; image reconstruction; medical image processing; random processes; tomography; Laplace-type operator; biological proteins; cryoelectron microscopy; data set; eigenvectors; graph Laplacian tomography; reconstruction algorithm; unknown random projections; Computed tomography; Density functional theory; Detectors; Image reconstruction; Laplace equations; Mathematics; Proteins; Reconstruction algorithms; Sampling methods; Ultrasonic imaging; Dimensionality reduction; graph laplacian; tomography; Algorithms; Computer Simulation; Image Enhancement; Image Interpretation, Computer-Assisted; Models, Statistical; Reproducibility of Results; Sensitivity and Specificity; Tomography, Optical;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/TIP.2008.2002305

Filename

4623181